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Coordinate patches on curved manifolds
by joda80
Tags: coordinate, curved, manifolds, patches
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Feb16-13, 06:56 PM
Dear All,
I've been studying differential geometry for some time, but there is one thing I keep failing to understand. Perhaps you can help out (I think the question is quite simple):
Can I use Cartesian coordinates to cover a curved manifold? I.e., is there an atlas that only contains Cartesian coordinate patches (I envision small squares covering a sphere, which should work if the squares overlap).
On the one hand I think this should be possible as the charts are allowed (and indeed, supposed) to overlap.
On the other hand, in classical diff.-geo. text books (not using manifolds), it says that no Cartesian coordinates are possible on curved manifolds.
How can these two ideas be reconciled?
Thanks a lot and best regards,
Feb16-13, 07:07 PM
C. Spirit
Sci Advisor
In general, a smooth manifold M has no single global chart i.e. a one element atlas [itex]\left \{ (M,\varphi ) \right \}[/itex] such that [itex]\varphi :M\rightarrow \mathbb{R}^{n}[/itex] is a homeomorphism. The classic example is [itex]S^{2}[/itex] which needs at least two charts (e.g. stereographic projection). However, given an arbitrary smooth manifold M, a maximal smooth atlas, and a smooth coordinate chart [itex](U,\varphi )[/itex] in the atlas, a cartesian coordinate representation [itex]\varphi (p) = (x^{1},...,x^{n})\in \mathbb{R}^{n}, p\in U[/itex] is certainly a possibility.
Feb16-13, 08:35 PM
See the difference global versus local?
Feb16-13, 11:09 PM
Coordinate patches on curved manifolds
Thanks for the responses! I understand. The motivation for the question was the role of "general coordinate transformations" in GR. The way I understand it is as follows:
We can use the local Cartesian coordinates to define tangent vectors, based on which we define the tangent space and tensors living in this space. The Cartesian patch and the associated tangent space represent the local inertial system. To obtain the covariant equations, we merely need to change the coordinates within this tangent space to something where the metric tensor is coordinate dependent. This includes coordinate systems that are accelerated and, by the equivalence principle, contain the effects of gravity. Now we take the SR equations and make sure they have the desired transformation properties. If they do, we have the laws that include the effect of gravity. Spacetime curvature isn't explicitly considered here at that stage. All these considerations could also be done in the Minkowski space (I think). The question is then, how does one infer a curved spacetime in the presence of gravity? (I thought it was because on a curved manifold the metric tensor is *also* coordinate-dependent, just as in the accelerated frames -- I think somewhere here might be my misunderstanding).
Feb16-13, 11:35 PM
C. Spirit
Sci Advisor
Well to start with, tangent vectors and tangent spaces are certainly not defined by using cartesian coordinates. They are coordinate independent constructions (of course). Let [itex]M[/itex] be a smooth manifold and [itex]p\in M[/itex]. A derivation at [itex]p[/itex] is a linear map [itex]X:C^{\infty }(M)\rightarrow \mathbb{R}[/itex] that satisfies [itex]X(fg) = f(p)Xg + g(p)Xf,\forall f,g\in C^{\infty }(M)[/itex]. We then define the tangent space [itex]T_{p}(M)[/itex] to be the set of all such derivations at [itex]p[/itex] and its elements as tangent vectors. Tensors are more general constructions that are still certainly not constructed explicitly from cartesian coordinates. What do you mean by the statement that making sure SR equations behave covariantly implies they take gravity into account? SR doesn't talk about gravity at all - we work in a globally flat space -time (Minkowski space). In SR we want to make sure equations are lorentz covariant; GR generalizes this vastly of course. If gravitational tidal effects are present then you can take two neighboring geodesics, connect them with a so called connecting / separation vector and see how they converge or diverge from one another by measuring the relative acceleration of one of the neighboring geodesics with respect to the other. This will allow you to measure the curvature by virtue of the equation of geodesic deviation.
Feb17-13, 12:22 PM
I dont seem to formulate very well where the problem lies.
So let me back up a bit: The way I understood the gist of general relativity (see e.g., Weinberg's approach in Gravitation and Cosmology) was that we start out on in flat space, where we know the equations of (SRT) are true. As we seek the equations in curved space (with gravity), we need to construct equations that transform like tensors under general coordinate transformations and yet reduce to the known SRT equations if the metric is flat. These general coordinates are needed because in curved space, Cartesian coordinates are impossible. E.g., we could take the equation of motion in Minkowski space and simply by using the covariant (instead of the ordinary) derivative, obtain the equation that is valid also in the presence of gravity (the geodesic equation). This viewpoint seems to be taken in Weinberg's Gravitation and Cosmology (e.g., pp. 105-106). Or do I misinterpret that?
If I didn't, then how do we embed these ideas in the context of manifolds? If I'm free to choose either Cartesian or any other coordinate system in my tangent spaces, then mathematically what is the difference between the local inertial system (=tangent space), an accelerated system (=tangent space with "general" coordinates, as in a rotating frame), and a system on a curved manifold with "true" gravity (which we can analyze only locally, i.e., also in a flat tangent space)? So if we always stay in flat tangent spaces with arbitrary coordinates, the role of general coordinate transformations isn't quite clear to me (it would be, if we could go from flat to curved space, but as we're stuck with tangent spaces, this isn't really possible ... or is it?).
It's amazing (and a little frustrating) how much you can read and presumably learn about this stuff and still miss some very basic notions... :-$
Feb17-13, 12:35 PM
C. Spirit
Sci Advisor
My first advice would be to not think of everything from the basis of cartesian coordinates. Yes what Weinberg is saying is correct of course: we want equations that are made up of covariant derivatives and tensor quantities so that if a physically relevant expression equals zero in one coordinate system, it equals zero in all coordinate systems. It is a mathematical way of stating that coordinates are nothing more than computational tools and that geometric objects exist independent of what coordinate basis they are represented in. So we have (1) general covariance and (2) the statement that if the lorentz metric is flat then such equations should reduce to equations satisfied in SR. You are also mixing up tangent spaces with coordinate charts. They are not the same thing. A coordinate chart consists of an open subset of the manifold and a homeomorphism to an open subset of euclidean space whereas a tangent space at a point is as defined in the previous post. Also I'm totally lost on your last few sentences because you are using tangent spaces in a wrong way (e.g. "flat" tangent space?). If you could clarify that last paragraph I would be much indebted. Thanks.
Feb17-13, 12:45 PM
C. Spirit
Sci Advisor
Just for some clarification, is your confusion one stemming from the physics or the math? If it is the latter as I suspect it is then I would suggest taking a look at proper math textbooks to learn the various differential geometry concepts because physics books tend to butcher these kinds of things and leave the reader confused.
Feb17-13, 01:15 PM
Indeed, I'm working with a couple of pure math books aside from physics books ... though mainly with Wald's "General Relativity", which seems to be rather clean/rigorous regarding the mathematical treatment. I think my problem is mostly of mathematical nature. If you're no bored yet, I'll give it another try:
Isn't one (standard?) way to construct a tangent space to use the coordinate lines given by the chart? This is how I interpret Wald's (General Relativity) exposition (p. 17): "Note that the above coordinate basis vector ##X_{\mu}## associated with a chart ##\phi## is the tangent to the curves on ##M## obtained by keeping all coordinate values except ##x_{\mu}## constant"). So the basis of the tangent space is related to the coordinate system. If we were to choose local Cartesian coordinates on the manifold, we would have a Cartesian basis in our tangent space, if we chose some curvilinear coordinates, the basis would no longer be Cartesian (which is fine, of course). But the tangent space is still Euclidean, irrespective of the coordinates used to construct the basis, isn't it? And I thought that "Euclidean space" is equivalent to a "space in which there is no gravity". So if indeed the tangent space is Euclidean, then how can we describe effects of gravity in this space.
Feb17-13, 02:09 PM
C. Spirit
Sci Advisor
Ahhh ok I see your confusion now mate. I first want to refer you to Lee's text on smooth manifolds to clear up later confusions (I absolutely love Wald to death but there are better ways to construct certain things). Let's take it from the top shall we? Let [itex]M[/itex] be a Hausdorff, second countable topological space (second countable so we can employ paracompactness which Wald does himself on occasion as you will see). We say that [itex]M[/itex] is locally euclidean of dimension n if [itex]\forall p\in M[/itex], [itex]\exists U\subseteq M[/itex] open and a map [itex]\varphi :U\rightarrow \mathbb{R}^{n}[/itex] such that [itex]\varphi [/itex] is a homeomorphism. We call [itex](U,\varphi) [/itex] a coordinate chart and the set of all coordinate charts covering [itex]M[/itex] an atlas. Furthermore, we shall now require that [itex]M[/itex] be a smooth manifold which means the atlas is now required to be a maximal smooth atlas i.e. [itex]\forall (U,\varphi ), (V,\psi )[/itex] in the atlas, [itex]\psi \circ \varphi ^{-1}:\varphi (U \cap V)\rightarrow \psi (U\cap V)[/itex] must be a diffeomorphism (these are called smooth transition maps and the charts are said to be smoothly compatible) and any chart smoothly compatible with all charts in the atlas is already in the atlas (the maximal part). You can certainly define the tangent space the way Wald does it but the way Lee does it is more instructive and makes you see you shouldn't care about the coordinates at all until computations come along.
Now, using notation more along the lines of Wald, for a given metric tensor [itex]g_{ab}[/itex] on our smooth manifold, there exists a unique torsion - free derivative operator [itex]\triangledown _{a}[/itex] such that [itex]\triangledown _{c}g_{ab} = 0[/itex] (you can do a similar thing for derivative operators with torsion c.f. problem 1 of chapter 3). Let [itex]\omega _{c}[/itex] be any dual vector field then we define the riemann curvature tensor by [itex]\triangledown _{a}\triangledown _{b}\omega _{c} - \triangledown _{b}\triangledown _{a}\omega _{c} = R_{abc}^{d}\omega _{d}[/itex]. Now let [itex](M,g_{ab})[/itex] be a space - time. We can describe what the curvature tensor does by showing it is related to how a vector parallel transported around a closed loop fails to return to its initial value and of course for this we need some region on the space - time (the pseudo - riemannian manifold). We do not detect it using nothing but [itex]T_{p}(M)[/itex]! What do we mean when we say the space - time is flat i.e. there is no presence of gravity? We simply mean that [itex]R_{abc}^{d} = 0[/itex] identically i.e. there is no curvature. This has nothing to do with the fact that [itex]T_{p}(M)[/itex] is isomorphic to [itex]\mathbb{R}^{n}[/itex]. Your only confusion is you are looking at the vector space - structure of the tangent space but when talking about curvature we are concerned with the pseudo - riemannian and smooth structure of the space - time.
Feb17-13, 02:21 PM
The tangent space is associated with each point of the manifold, what kind of effects of gravity do you want to describe at a point? There aren't any.
Maybe in this phrase from another of your posts lies most of your confusion: " This includes coordinate systems that are accelerated and, by the equivalence principle, contain the effects of gravity."
Actually coordinate systems don't contain the effects of gravity, because they don't contain any physical effect at all, they're just labels that can always be used locally due to how manifolds are mathematically defined.
Also it is not strictly correct to call tangent spaces Euclidean, in (pseudo)Riemannian manifolds like it is the case in GR, tangent spaces associated to the points of the manifold have an inner product that is not Euclidean in general (it is not in the case of GR). Don't mix this with the property that this space is flat to first order approximation and therefore locally isometric to the manifold's point neighbourhood and to R^n. Note depending on the level of the structure I want to highlight I coud use different terms here, if thinking only of the vector space structure of the tangent space, I'd say isomorphic to R^n, if I was stressing the smooth structure I'd say diffeomorphic to R^n, since I'm stressing the pseudoRiemannian case (you are interested in GR) I say locally isometric to R^n.
Feb18-13, 04:00 PM
Thanks, guys! I think I understand (the metric tensor and the curvature are properties of the manifold, not of the tangent spaces; accordingly, the coordinates chosen to describe the tensors merely determine their components, not the tensors themselves, which of course is the purpose of tensors).
Why cant gravity be defined at a point on a manifold after all, were dealing with differential equations that are valid (only) at a point (the curvature tensor is also a *local* property of the manifold or isnt it?).
The statement about the coordinate systems, and in fact, the role of coordinate transformations still confuse me. I understand that physics is independent of the coordinate systems, but isn't it true that an observer in a freely falling elevator in a gravity field observes no gravity, while an observer in an accelerated system in free space does feel gravity (this is what Einstein called the 'happiest thought of his life'). I would suspect that it depends on what quantities were considering. A Riemann tensor in spacetime is independent of the coordinates, but the acceleration in ℝ##^3## is not. This is why were interested in Riemann-tensor formulations, after all, because only they have the desired objectivity.
I still have some difficulty conceptualizing the roles of the coordinate transformations and general covariance in the manifold perspective. Per Walds Appendix C1, these coordinate transformations are equivalent to maps between two manifolds. I could think of two interpretations:
a) We are in free space, where there is no gravity. Accordingly, the laws of SR hold. Now we do a transformation to an accelerated coordinate system and construct equations that transform in the desired way. The fact that we can associate the coordinate transformation with the effect of gravity is based on the equivalence principle. This is the passive interpretation of the local diffeomorphism in Walds App. C1.
b) Alternatively, we can take an active perspective and map the tensors from a manifold with vanishing curvature to one that is curved, and again expect the tensors to transform in the desired manner (however, we would have to require that the tensors dont change during the process).
Do any of these interpretations make any sense? (If not, how do you look at these things?).
I really appreciate your patience!
Feb18-13, 04:59 PM
C. Spirit
Sci Advisor
(b) is wrong; we are concerned with diffeomorphisms and you cannot make the curvature of a riemannian manifold vanish identically with a diffeomorphism. As for your first point, this goes way back to simple calculus in [itex]\mathbb{R}^n[/itex]. Let [itex]f:U\rightarrow \mathbb{R}^m[/itex] be a map where [itex]U\subseteq \mathbb{R}^n[/itex] is open. Let [itex]a\in U[/itex] then we say [itex]f[/itex] is differentiable at [itex]a[/itex] if there exists a linear map [itex]D[/itex] such that [itex]lim_{h\rightarrow 0}\frac{f(a + h) - f(a) - Df(a)}{\left \| h \right \|} = 0[/itex]. This is just the familiar calculus definition. Do you remember your epsilon delta definition of limits of functions? We required the use of open balls. You can't use nothing but a point and no extra information whatsoever to talk about these things. Manifolds are no different in spirit; local is not exactly a mathematically defined term but it is usually used when talking about properties true for neighborhoods of points e.g. local compactness, local connectedness / path connectedness, local continuity, locally euclidean etc.
EDIT: Read chapter 4 of Wald, it should clear things up for you.
Apr4-13, 09:54 PM
Just to follow up: I think I found out what my misunderstanding was. Somehow I thought that the coordinate systems on a manifold were always the Riemann normal coordinates (i.e., valid only in a small neighborhood of a given point). Accordingly, I thought all coordinate systems were describing local inertial frames, and doing transformations from one inertial frame to another didn't seem like what we want in general relativity. But I've now convinced myself, hopefully not in error, that the global* curvilinear coordinates compatible with the curved manifold are just as valid a choice for the coordinates (the definition of the manifold only says that there need to exist open subsets of M that can homeomorphically be mapped into R^n, not that these subsets need to cover only infinitesimal neighborhoods). This should solve my problem of how to fit the global/curvilinear coordinates into the manifold picture.
Cheers ...
* I assume a well-behaved, albeit "warped" spacetime structure, like a warped 2D surface for which there should always be one global curvilinear coordinate system that can be mapped via a homeomorphism into R^2, right? (Well, my point is merely that it doesn't need to be valid only in a small neighborhood of a point.)
Apr4-13, 10:29 PM
Sci Advisor
Consider what it would mean to put global coordinates on some surface. Since the coordinate patch is homeomorphic to R^2, and the coordinate patch covers the entire surface, then the whole surface must be homeomorphic to R^2. This only works if the surface is R^2. If the surface is, say, a sphere, then you'll have to cut a hole in it somewhere to map it onto R^2 (and this violates the definition of what makes a homeomorphism).
But taking the sphere example, the standard longitude and lattitude coordinates cover most of the sphere, except for the north and south poles, and the international date line. These are all points where the definition of "homeomorphism" is violated, because multiple different coordinate values correspond to the same point on the manifold.
So here's a case in which there is a coordinate chart that covers almost all of a manifold, but is still not global. In general, there does not need to exist any global chart. In fact, the existence of a global chart imples that the whole manifold is homeomorphic to some R^n. Hence if the manifold is not homeomorphic to R^n, there cannot be a global chart.
Apr4-13, 11:38 PM
C. Spirit
Sci Advisor
Apr5-13, 06:37 AM
Thanks ... I knew I was going to get in trouble for using the word "global" ;) Point taken! Just as a check, though: Let's assume a 2D surface that looks like this:
(from www.bu.edu)
And let's also assume that this image repeats itself periodically in space in x- and y-directions. Wouldn't a curved surface like this have a single curvilinear global system (I think it can uniquely be mapped to R^2).
EDIT: Updated the URL (the original ones didn't wotk for some reason)
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text:
ST. LOUIS COUNTY, MO (KPLR)-There was fire on the tarmac at Lambert Airport Saturday morning, but passersby didn't need to call 9-1-1. Crews were conducting an emergency drill designed to train staff in case of a crash.
Crash drill underway at Lambert. @FOX2now http://t.co/jd98bQCXBL—
George Sells (@GeorgeSells) April 19, 2014
It was just this past fall that airport officials ran a similar drill. The fire is set in a mockup of a fifty foot airplane fuselage. Then the crews go to work. Airport firefighters, airline employees, and even two area hospitals are part of this drill, which the FAA requires at least every three years.
@FOX2now http://t.co/tVcSQnTP0j—
George Sells (@GeorgeSells) April 19, 2014
There is no word from Lambert on why two of the drills are being conducted so close together. Regardless, officials told us the last time around that the training is vital in keeping everyone on prepared if catastrophe were ever to strike. Doing this work is non-negotiable.
The drill lasted from 10:00am until Noon, so if you saw smoke near the airport there was no need to worry.
ALERT: We will have a simulated aircraft fire on the runway over Lindbergh, Sat., 4/19 frm 10am-noon. It's an emergency training exercise.—
Lambert-STL Airport (@flystl) April 18, 2014


text:
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Locate the right contact, dealer or service partner worldwide
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text:
Just after 7:30 PM Saturday, Fergus Falls Police got a call about a threat that had been called in to the store. The employee who took the call says the caller made specific threats towards employees and customers. Exact details on the type of threat is not being released at this time. The store was evacuated, officers did a sweep and found no threat. The store was closed for about two hours and reopened.
Walmart security and the FFPD are working to see if this was an isolated incident. An investigation is underway.
The FFPD would like to stress that no one was hurt, no one was taken hostage and no one was found displaying a weapon in the store.
The Fergus Falls Wal-Mart was evacuated Saturday evening. Multiple law enforcement agencies were called in. The Otter Tail County Sheriff's Department says no one was hurt, and that more information is expected to come throughout the evening.


text:
The Primary Group is selective in choosing our strategic alliances, enabling us to commit more time and resources to our established clients. We recognize that our clients are making significant investments in quality talent, and we honor that commitment with the degree of responsiveness and. . . [read more]
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The Primary Group is an industry-leading executive search firm that boasts over 30 years of experience, combined with an unparalleled commitment to excellence. Whether your recruiting needs fall under the spectrum of sales, marketing, management, operations, or any executive . . . [read more]


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Tom Mens, Tom Tourw?, "A Survey of Software Refactoring," IEEE Transactions on Software Engineering, vol. 30, no. 2, pp. 126-139, February, 2004.
@article{ 10.1109/TSE.2004.1265817,
author = {Tom Mens and Tom Tourw?},
title = {A Survey of Software Refactoring},
journal ={IEEE Transactions on Software Engineering},
volume = {30},
number = {2},
issn = {0098-5589},
year = {2004},
pages = {126-139},
doi = {http://doi.ieeecomputersociety.org/10.1109/TSE.2004.1265817},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
RefWorks Procite/RefMan/Endnote
JO - IEEE Transactions on Software Engineering
TI - A Survey of Software Refactoring
A1 - Tom Mens,
A1 - Tom Tourw?,
KW - Coding tools and techniques
KW - programming environments/construction tools
KW - restructuring
KW - reverse engineering
KW - and reengineering.
JA - IEEE Transactions on Software Engineering
Abstract—This paper provides an extensive overview of existing research in the field of software refactoring. This research is compared and discussed based on a number of different criteria: the refactoring activities that are supported, the specific techniques and formalisms that are used for supporting these activities, the types of software artifacts that are being refactored, the important issues that need to be taken into account when building refactoring tool support, and the effect of refactoring on the software process. A running example is used throughout the paper to explain and illustrate the main concepts.
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1. MXR Blue Box
Looking for some excitement? This unassuming little box shovels out enough low frequencies to frighten a blue whale! more info$79.99 — Save $46.34 (36%) add to cart
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Effects pedal. Made by MXR. (MC.MXR-103)
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Christmas is now a warm and delightful memory, and everyone is looking forward to ringing in the New Year with fireworks and parades. High school football champions have long since been determined. Congratulations to the Rebels and Tornados for an outstanding season! We know where our favorite college teams are headed for their post-season play. And, every football fan is watching to see who will play in Super Bowl MXLVIII! Sorry, I am sure everyone knows it is really XLII, the 42nd Super Bowl. Surely, there is nothing else to occupy our time during this break between Christmas and New Years.
Except, if you manage your own investments, this should be a week filled with number crunching, phone calls, projections, as well as buys and sells in your investments. While those managing taxable accounts with less than fifty or a hundred thousand may not be as active, those with larger taxable accounts should be. If you do not manage the accounts on your own but have a manager, you should make sure they are not on vacation during this critical week. If they are, you are most likely missing out on significant tax planning opportunities.
While the indexes such as the Dow Jones Industrial 30 or the S&P 500 have not performed exceptionally well this year, you may find the dividends and capital gains paid from your mutual funds to be higher than normal. While every fund will vary and few generalities can be used, this is an area you should review closely. This year will be remembered by many investment managers due to the number of highs that occurred during the year, only to be followed by significant corrections. For some mutual funds, this rollercoaster ride increased trading activities; and for others, it may have caused positions held for years to be partially or entirely sold.
If you are wondering why this is important, you must first understand the rules mutual funds follow. The capital gain distribution a mutual fund pays near the end of the year has nothing to do with performance for the year. Tax law specifies that a mutual fund must distribute in the form of a dividend ninety percent of their realized gains. This means, if a mutual fund has gone up in value during the year but sold very few positions to "realize" their profits or "gains" then, the capital gain distribution will not be very large. However, if the fund due to market volatility sold some or many of their positions and "realized" the gains, even if their performance for the year is low or a loss, the capital gain distribution could be very large. And if the shares are held in taxable accounts, then you will receive a 1099 and have higher income to report on your annual tax return.
The question becomes, are there steps you can take to assist in managing the tax bite taxable investment accounts may create? And, this leads us back to how busy the week between Christmas and New Years can be for investment managers that not only manage the investments, but who also manage for their clients' tax impact such as Quality Financial Concepts (QFC) and I am sure others.
During this time, you should review the capital gains and losses you have already "realized" for the year. To do this, you should add the capital gains that have already been paid by mutual funds and estimate the gains to be paid on the last few trading days of the year. Once you know your tax impact from these gains, a review of your portfolio should take place. If you are sitting with substantial gains, you should look to see if there are any positions that if sold would help offset these gains. This includes mutual funds as well as stocks.
For mutual funds, there are two important numbers you should track. The first is the amount of money you placed in the fund. You will add to this amount if you make additions to the fund and subtract from this value the amount of any withdrawals you take from the fund. This is the easy way to see if you are up or down in a fund by comparing this "net invested" amount to the fund's value. The second number is the tax basis. This starts out being the amount you originally invested in the fund, but then it is adjusted for any reinvested dividends or capital gains, as well as for any withdrawals taken. It is very possible for the fund's value to be higher than the net amount invested, thus you have made money; but for the tax basis to be more than the fund's value and thus if the fund was sold, you would have a tax loss to take on your tax return.
Professional managers will track this number and can make decisions during the last week of the year to help manage the tax impact their clients will have. So, do not miss this important opportunity to manage the potential tax impact your taxable investment accounts may create.
Would you like a response to a financial question? Send your question to Doug Horn, 115 W. Broadway, Maryville, TN 37801. Be sure to mark your envelope Money Matters.
Doug Horn, CFP, is an area financial planner with more than 24 years financial experience and founder of Quality Financial Concepts, located in downtown Maryville on Broadway.
Doug Horn, CFP, Registered Investment Advisor in Tennessee and Texas and Registered Principal, Branch Office of and Securities offered through CUE Financial, Member FINRA, SIPC.


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WASHINGTON - The Justice Department today announced an agreement with the city of Humboldt, Kan., to improve access to all aspects of civic life for individuals with disabilities. The agreement was reached under Project Civic Access (PCA), the department's wide-ranging initiative to ensure that cities, towns and counties throughout the country comply with the Americans with Disabilities Act (ADA). The department has now reached 197 agreements under the PCA initiative, improving access to civic life for more than four million individuals with disabilities nationwide. According to census data, the city population is just under 2,000, and just over 21 percent of Humboldt residents have a disability.
"Individuals with disabilities must have the opportunity to participate in civic life in every city, town and county in the country, no matter how large or small, and this agreement represents another positive step forward," said Thomas E. Perez, Assistant Attorney General for the Civil Rights Division. "We applaud Humboldt officials for their commitment to improving access for all residents and visitors with disabilities to the full range of city programs, activities, services and facilities."
"Kansans with disabilities have much to contribute," said Barry Grissom, U.S. Attorney for the District of Kansas. "This agreement will help remove the barriers that prevent them from participating fully in community life. I am pleased this matter was resolved without protracted litigation."
PCA was initiated to ensure that persons with disabilities have an equal opportunity to participate in civic life, a fundamental part of American society. As part of the PCA initiative, Justice Department investigators, attorneys and architects survey state and local government facilities, services and programs in communities across the country to identify the modifications needed for compliance with ADA requirements. The agreements are tailored to address the steps each community must take to improve access.
Under the agreement announced today, Humboldt officials will take several important steps to improve access for individuals with disabilities, such as:
Today's agreement was reached under Title II of the ADA, which prohibits discrimination against individuals with disabilities by state and local governments. The department will actively monitor compliance with today's agreement, which will remain in effect for three years from Feb. 8, 2012, or until the department has confirmed that all required actions have been completed, whichever is later.
People interested in finding out more about the ADA, today's agreement, the PCA initiative, or the ADA Best Practices Tool Kit for State and Local Governments can access the ADA website at www.ada.gov or call the toll-free ADA Information Line at 800-514-0301 or 800-514-0383 (TTY).
The agreement with the City of Humboldt is available at http://www.ada.gov/humboldt_KS_pca/humboldt_KS_sa.htm.
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Body by Reutter 4 cylinder Period correct replacement engine-unnumbered case 4 speed manual transmission Only 1617 Cabriolets produced Original body panels with numbers Beautiful almost new soft top and matching... More
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