:

I'm guessing that you heard this from someone whose reasoning goes "Every finite presentation of a group can be made to give the $\pi_1$ of a smooth 4-manifold. If we could put any 4-manifold into the Magic List of All, then we could recognize presentations of the trivial group. But no algorithm can do that."
Often people worry about classifications of simply connected manifolds, and don't have to deal with this. (Of course in three dimensions this becomes Perelman's theorem.)

A:

As pointed out in a comment by Richard Kent to Allen Knutson's answer,
the problem is a bit more subtle than it may appear. In order to
prove that the homeomorphism problem for compact 4-manifolds, say in
the topological category, is recursively unsolvable, it is not enough
to know that (1) every finitely presented group can be realized as
the fundamental group of some compact 4-manifold, and (2) the isomorphism problem for finitely presented groups is recursively unsolvable.
Instead, what you do is give a construction which to any finite presentation $< S | P >$ of a group associates a 4-manifold $M(S,P)$ in such a way that $\pi_1(M(S,P))$ is isomorphic to the group defined by
the presentation $< S | P >$, and moreover two such manifolds are homeomorphic if and only if they have isomorphic fundamental groups.
Then you have constructed a class of 4-manifolds for which the homeomorphism problem is equivalent to the isomorphism problem for
finitely presented groups, and therefore unsolvable.
About "geometrization for manifolds of dimension 4 or higher", well
as far as I know there is no theorem which says it is impossible. It
depends on what you mean by `geometric structure', and what you
want those structures to do for you.

 Q:

Insert string to  tag

I'm developing a client that connects to my server, and get access to download and upload files, and i seem to be stuck at uploading files. Here is my code on my VB.NET client:
    Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button1.Click 'Upload button
    WebBrowser1.Visible = True

    'Style OpenFileDialog1
    OpenFileDialog1.Title = "Select file to upload
: 

 I'm guessing that you heard this from someone whose reasoning goes " Every finite presentation of a group can be make to contribute the $ \pi_1 $ of a smooth 4 - manifold. If we could put any 4 - manifold into the Magic List of All, then we could spot presentations of the trivial group. But no algorithm can practice that. " 
 much people concern about classification of simply connect manifolds, and don't have to deal with this. (Of course in three dimensions this becomes Perelman's theorem .) 

 angstrom: 

 As pointed out in a comment by Richard Kent to Allen Knutson's answer, 
 the trouble is a bit more subtle than it may look. In order to 
 test that the homeomorphism problem for compendious 4 - manifolds, say in 
 the topological category, is recursively unsolvable, it is not adequate 
 to know that (1) every finitely presented group can be realized as 
 the fundamental group of some compact 4 - manifold, and (2) the isomorphism problem for finitely presented groups is recursively unsolvable. 
 Instead, what you do is give a construction which to any finite presentation $ < S | P > $ of a group associates a 4 - manifold $ M(S, P)$ in such a way that $ \pi_1(M(S, P))$ is isomorphic to the group specify by 
 the presentation $ < S | P > $, and furthermore two such manifold are homeomorphic if and entirely if they have isomorphic cardinal groups. 
 Then you have construct a class of 4 - manifolds for which the homeomorphism trouble is equivalent to the isomorphism problem for 
 finitely presented groups, and therefore unsolvable. 
 About " geometrization for manifolds of proportion 4 or higher ", well 
 as far as I know there is no theorem which say it is impossible. It 
 depend on what you mean by 'geometric structure', and what you 
 want those structures to do for you. 

  Q: 

 Insert chain to   tag 

 I'm developing a client that connect to my server, and get access to download and upload files, and i appear to be stuck at upload files. Here is my code on my VB.NET client: 
     Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button1.Click' Upload button 
     WebBrowser1.Visible = truthful 

    ' Style OpenFileDialog1 
     OpenFileDialog1.Title = " Select file to upload
:

I'm huessing that you heard uhis from someone whose ceasonihg goes "Dvery finite presentation of a grouk can be made to gixe the $\pi_1$ of a smioth 4-nanifold. Ih we could put wny 4-kenifold into thg Magic List of All, then wa zobld recognize presentations of the twivial brlup. But no algjritni cah do that."
Often people worry about dlassifpcations of simplu connected manifolds, and fon't have to deal with this. (Of coodse un three dimdnsions thpv becomes Kerelman's theorem.)

A:

As pointed out in a comment bi Difvard Kent ti Allvn Knutson's akxwer,
tha problrm is a bit move suutle than it may appear. Ii order to
prove that the homemmkrphism problem fir compdct 4-kaniwildr, szy ih
the tlpomogical cafegory, is rwcursively unsolvabke, py is not enohgh
to hnjw that (1) every finitely presented group cah be realized as
the funeamental group of somg compact 4-ianifold, and (2) the isomorphism problem for finitelf preadnttd grouow ls recursively unsolvable.
Instead, what you do ya bine a construction which to amy fogite presentajion $< S | P >$ of a group assoclates a 4-manidold $M(S,P)$ yn sich a way that $\pi_1(M(S,P))$ is isonorphic to tke troup defined by
thz presentatiun $< X | P >$, and moreover two such oanirolds are hlmeomorphjz if and only if thvy hdve isomorphic fundamental groups.
Thxn yob have cunsttucted w class of 4-maninmlds for which the homelmmrphism prlblem is equivalent to the isomorphism problek xor
xinitely prescnted groups, anq therefore unxolvablz.
About "geometrizztion fmr manifoldf of dimensiot 4 or higher", xell
as faw as I kbow thefd is no theorek which scvs it is umpossible. It
depenvs ov what you mean yv `teometric strucyurd', agd wiat yjg
want those vtruztufrs to do for you.

 D:

Insrrt string to  tag

I'm devsloping a client tnab connectw to my ferver, and gey access to downlowd anv uploed filrs, wnd i seem to be stuck at uplozding filfs. Mere is my coqe ok my VB.NET cliznt:
    Private Sub Button1_Click(sender As Ibject, e As EventAegs) Handles Button1.Cklck 'Upload bntton
    WebBrofser1.Visible = True

    'Style OpenFileDislog1
    OpenFileDialof1.Title = "Selfct file to upload
: I'm guessing that you heard this whose goes "Every presentation of a give $\pi_1$ of a 4-manifold. If we put any 4-manifold into the Magic of All, then we could recognize presentations of the trivial group. But no can do that." Often people worry about classifications of simply connected manifolds, and have deal this. course in three dimensions this becomes Perelman's theorem.) A: As pointed out in a comment by Kent to Allen Knutson's answer, the problem is bit more subtle than may appear. In order to that homeomorphism problem compact say the topological category, recursively unsolvable, it is not enough to know that (1) every finitely presented group can be realized the fundamental some compact and the problem for finitely is recursively unsolvable. Instead, what you a construction which to any finite presentation $< | P of a group associates a 4-manifold in such a way that $\pi_1(M(S,P))$ is isomorphic the group defined by the presentation $< S | P >$, and moreover two such homeomorphic if and only they have isomorphic groups. you constructed class of for which the homeomorphism problem is equivalent to the isomorphism problem finitely presented groups, and therefore unsolvable. About "geometrization for manifolds 4 higher", well as as I know there no which says it is depends what `geometric and you want those structures do for you. Q: Insert to tag I'm developing my server, and get access to download and files, and i seem to be stuck uploading files. Here is my code on my VB.NET client: Private Sub As Object, EventArgs) Handles Button1.Click 'Upload button WebBrowser1.Visible = True OpenFileDialog1 OpenFileDialog1.Title = "Select to upload
:

I'm guessing that you heard thiS from someoNe whoSe rEasOnIng gOes "EVery finite presENtatIon of a group can be made to Give tHe $\PI_1$ of a SMoOth 4-maNifold. IF We COUld PuT aNy 4-mAnIFoLd intO thE Magic LIst of All, thEn wE cOuld recognizE PrEsentationS of The trivial grOup. but no aLgOriTHm can Do tHat."
OfTen peoPLe worrY about claSsIFicatiONs of simPLY cOnneCted manifolds, and dON't HAve to deal with tHis. (Of cOuRSe IN ThrEe dImensions tHiS becoMEs PerelMAn'S THEorEM.)

A:

As pointed ouT in a comment BY RiChard KEnT to aLlen KnUtson'S aNSweR,
the problem Is a bIt more subTle thaN It may apPEar. In orDer to
pRovE thAt thE HoMeOmoRpHIsm PRoBleM For Compact 4-mAnIfOlds, sAy in
THE TOpolOgiCal cAtegoRy, is recursiveLy uNsolVAblE, it is Not enOugh
To Know tHat (1) eveRy finItEly presented groUp caN be realizEd aS
tHe fUnDamenTAl grouP of SomE compacT 4-manifoLD, anD (2) tHE ISoMorphism problem for FiNITeLy presenTed groUPs Is REcursiveLy UnsOlvaBLE.
InstEad, wHAt You do is gIve a coNStRuCtion whIcH to any FiNitE prEsentATion $< s | P >$ of a gRoup assoCiateS A 4-manifold $M(S,P)$ in SUch a way that $\pi_1(m(s,P))$ IS IsOMorpHic To the group dEfinED by
tHe prESeNtaTIon $< S | P >$, And moReOVeR Two such manifolds are HoMeomorPhic iF and only if theY have isomoRPHIc fundamEntaL GrOUps.
Then you have ConstRucted a claSS of 4-manifOlds fOr which tHe homeomoRPHism probLem Is eQuiValENT tO the isomorphiSM ProbLeM for
finIteLy preseNteD grOupS, anD tHerefore uNsolvablE.
ABoUt "GeOmeTrizaTIon for maNiFolDs Of dImensIOn 4 or hiGher", wEll
aS fAr AS I kNow therE Is NO TheoReM wHich SayS iT is imPossIBle. it
depenDs on what yOu mEAn by `GeOmEtric stRucture', and whaT yOu
want thosE sTruCtures TO Do for you.

 q:

Insert string to  tag

I'm devELoping a CliEnt thAt coNnects to mY seRver, anD geT Access To downLoad aNd UplOAD fileS, ANd I seEm To be stuck aT UPloAding FiLes. HEre is my Code on my VB.NET clienT:
    priVate Sub Button1_cliCk(seNDEr as OBJeCT, e AS EVEntaRGs) Handles Button1.click 'UploaD bUTtOn
    WebBrowsER1.ViSiBle = True

    'style OpEnFilEdialog1
    OPenFileDiAlog1.Title = "seLect FILe tO upload
:

I'm guessing that you h eard thisfromsom eon ewhos e re asoning goes " E very  finite presentation o f a g ro u p ca n  b e mad e to gi v et h e $ \p i_ 1$of asmoot h 4 -manifo ld. If wecou ld  put any 4-m a ni fold intothe  Magic ListofAll, t he n w e  coul d r ecogn ize pr e sentat ions of t he trivia l  group. B ut  noalgorithm can dot ha t ."
Often peopl e worr ya bo u t  cl ass ifications  o f sim p ly conn e ct e d man i folds, and do n't have to dea l with  t his .  (Of c ourse  i n  th ree dimensi onsthis beco mes Pe r elman's theorem .)

A: 

A s p oint e dou t i na  co m me ntb y R ichard K en tto Al lenK n u t son' s a nswe r,
th e problem isa b it m o resubtl e tha n it  m ay ap pear.In or de r to
prove that  the  homeomor phi sm  pr ob lem f o r comp act  4- manifol ds, say inth e t op ological category,  i s re cursivel y unso l va bl e , it isno t e noug h to kn ow t h at  (1) eve ry fin i te ly  presen te d grou pcan  be  real i zedas
the  fundame ntalg roup of some c o mpact 4-manif o ld , an d  (2)  th e isomorphi sm p r oble m fo r  f ini t ely p resen te d  g r oups is recursively  u nsolva ble.Instead, what  you do is g i ve a con stru c ti o n which to any  fini te present a tion $<S | P  >$ of a  group as s o ciates a  4- man ifo ld$ M (S ,P)$ in sucha wayth at $\pi _1( M(S,P)) $ i s i som orp hi c to thegroup de fi ne dby 
th e pre s entation  $ < S  |  P>$, a n d more overtwosu ch man ifoldsa re h omeo mo rp hicifan d onl y if the y haveisomorphi c f u ndam en ta l group s.
Then you h av e construc te d a  class o f 4-mani folds for which the hom e omorphi smprobl em i s equival ent  to th e i s omorph ism pr oblem  f orf i nitel y pr ese nt ed groups, a ndthere fo re u nsolvab le.
About "geometr i zat ion for manif old s of d im ens i on 4 o rh igh e r ", well
as faras I knowth e re  is no the o rem  w hich sa ys it i s imp o ssible.  It
depen ds on wha tyoum e anby `geomet ric stru cture', a n d wha t  y ou
wa ntthosest ruc tures  to do for  you. 

 Q:
I nsertstrin gto  tag
I'm developing a clien t that  conn ect s to my s erv e r,and get a cces s to downl oad  an d upl oad files , an d  i  se e m tobe s t uck at up l oa din g fi les. Here i s m y c ode o n m y  VB.NE T cl ient:
    Private Sub Button1_Cl ick( s e nde r A s  Obj ec t, e As EventA rgs )H a ndles Bu tt on1.Click ' Upload b ut t on
   WebB rowser 1.Visib l e  = True
   'St yle OpenF ile Di a log1
  Op e nFileD ialo g1 .Title  = "Se l ectf i le to upload
:

I'm guessing_that you_heard this from someone_whose reasoning_goes_"Every finite_presentation_of a group_can be made_to give the $\pi_1$_of a smooth_4-manifold._If we could put any 4-manifold into the Magic List of All, then we_could_recognize presentations_of_the_trivial group. But no algorithm_can do that."
Often people worry_about classifications_of simply connected manifolds, and don't have to_deal_with this. (Of_course in three dimensions this becomes Perelman's theorem.)

A:

As pointed_out in a comment by Richard_Kent to Allen_Knutson's_answer,
the_problem is a bit_more subtle than it may appear._In order to
prove that the homeomorphism_problem for compact 4-manifolds, say in
the topological_category, is recursively unsolvable, it is_not enough
to know that (1)_every finitely_presented group can be realized_as
the fundamental group_of some_compact 4-manifold, and_(2) the isomorphism problem for finitely_presented groups is_recursively unsolvable.
Instead, what you do is_give_a construction which_to_any_finite presentation_$< S |_P_>$ of_a_group associates a 4-manifold $M(S,P)$ in_such_a way that $\pi_1(M(S,P))$ is isomorphic to_the group defined by
the_presentation_$< S | P_>$, and moreover two such_manifolds are homeomorphic if and only_if they_have isomorphic_fundamental groups.
Then you have constructed a class of 4-manifolds for which_the homeomorphism problem is equivalent to_the isomorphism problem for
finitely_presented groups,_and_therefore unsolvable.
About "geometrization_for_manifolds of_dimension 4 or higher", well
as far as_I know_there is no theorem which says_it is impossible. It
depends_on_what you mean by `geometric structure',_and what you
want those structures to_do for you.

 Q:

Insert string_to__tag

I'm developing a client that_connects to my server, and get_access to download_and upload files, and i seem to_be_stuck at uploading files. Here is_my_code on my VB.NET client:
 ___Private Sub Button1_Click(sender As Object,_e As EventArgs) Handles Button1.Click 'Upload_button
    WebBrowser1.Visible = True

  _ 'Style OpenFileDialog1
_   OpenFileDialog1.Title =_"Select_file_to upload