# Daniel Asimov

less info
reputation
313
bio website location University of California, Berkeley age 67 member for 4 years seen Mar 24 at 1:18 profile views 896

# 73 Actions

 Nov15 awarded Nice Answer Oct10 awarded Yearling Sep30 awarded Nice Answer Jun25 awarded Excavator Jan11 revised Examples of common false beliefs in mathematics. it's -> its Jan11 comment Are there smooth bodies of constant width? I took a look at the Fillmore paper, and just before his Corollary to Theorem 2 -- which reads "Corollary. There exists an analytic hypersurface of constant width in E^n having the same group of symmetries as a regular n-simplex." -- he writes "If we imitate the construction of a Reuleux triangle . . .. Thus:" This seems to imply that he is assuming that [the intersection of four balls in 3-space, centered at the vertices of a regular tetrahedron and each with radius = the side-length of the tetrahedron] is a body of constant width. But this is known to be false. Dec24 comment $SU(2)$ and the three sphere It's not so much that you also need det(x) = 1, as that this is exactly the same as saying |a|2 + |b|2 = 1. Sep14 comment Riemann zeta at even integers In the functional equation for ζ(s), the term Γ(s) should be Γ(s/2), and the term Γ(1-s) should be Γ((1-s)/2). Aug13 comment Irreducible homology 3-spheres that bound smooth contractible manifolds The usual contractible 2-complex discovered by Bing is called a "House With Two Rooms", and this is not what is depicted in the image above this answer. The 2-complex depicted is not contractible (since a loop around either inner cylinder is a nontrivial 1-cycle, as is easily verified). To obtain the House With Two Rooms, one needs to add two disjoint rectangles IxI to the image, each one intersecting one inner cylinder in an interval, the outer cylinder in an interval, and the 2-complex depicted in its entire (rectangular) boundary circle. Mar28 awarded Yearling Mar29 awarded Yearling Feb25 awarded Nice Answer Jan12 awarded Nice Answer Oct25 awarded Nice Answer Aug25 revised Infinite-dimensional complex polynomial or rational Lie algebras and their pseudogroups changed title Aug25 revised Infinite-dimensional complex polynomial or rational Lie algebras and their pseudogroups Added note about the ease of computing formulas for the flows Aug25 revised Infinite-dimensional complex polynomial or rational Lie algebras and their pseudogroups probably -> surely Aug25 asked Infinite-dimensional complex polynomial or rational Lie algebras and their pseudogroups Aug16 comment How well can we localize the “exoticness” in exotic R^4? Removing a standard $D^4$ from a potentially-exotic smooth $S^4$ yields a potentially-exotic $\mathbb{R}^4$ that's standard at infinity. So if it were known that the latter must be globally standard, then replacing the $D^4$ would imply the original $S^4$ is standard, and hence the 4-dimensional smooth Poincaré conjecture. And there's essentially only one way to replace the $D^4$, since Gamma_4 = 0 (Cerf) implies oriented diffeos of $S^3$ are smoothly isotopic. Aug15 comment Measure on real Grassmannians For one application, an explicit curve {C(t) : t in [0,oo)}, dense in a Grassmannian of 2-planes in n-space, is the basis for the animation technique in statistical computer graphics known as the Grand Tour. It's important to ensure that as t -> oo, the curve C spends time in any open set U proportional to the invariant measure* of U. * Though the invariant measure on a Grassmannian is unique up to a scalar multiple, the invariant metric is not in the sole case of 2-planes in 4-space. This oriented Grassmannian's metric is the product of two round 2-spheres whose radii may be in any ratio.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.923154890537262, "perplexity": 1353.8756459260364}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609538423.10/warc/CC-MAIN-20140416005218-00429-ip-10-147-4-33.ec2.internal.warc.gz"}