26,131 reputation
166153
bio website rybu.org
location Victoria, BC
age 41
visits member for 5 years, 9 months
seen yesterday
I'm a professor of mathematics at the University of Victoria, in BC Canada.

Jul
29
awarded  Nice Answer
Jul
19
reviewed Close Derivative of Band-limited functions
Jul
10
comment Reference request concerning PL tangent Stiefel-Whitney classes
I haven't thought about this much, but for a PL microbundle can't you just re-encode the linear-independence language in terms of matroids, which seems to make sense once you standardize the PL-micro bundle to a genuine plane bundle with a PL structure. So doesn't it just follow from Kister's 1964 paper?
Jun
25
comment Riemann mapping theorem for homeomorphisms
The Schoenflies theorem isn't particularly hard to prove. There's a nice cut-and-paste style argument given in Hatcher's 3-manifolds notes.
Jun
17
comment What's the detailed proof of “the composition of planar tangles is well-defined”?
I'm kind of swamped reconstructing my house at present so I'm not logging in very much (let alone talking math with other human beings often). But I'd be happy to go into more details in one-on-one conversations.
Jun
5
reviewed Close $E_n$ structures on Symmetric Monoidal Stable infinity-categories
Jun
5
reviewed Close Binary Quadratic Forms with coefficients in $F_q[T]$
Jun
2
reviewed Close relations in (\mathbb P^1)^n
Jun
2
reviewed Leave Open Searching for $C^*$
Jun
2
reviewed Close Closed form for binomial coeff sum
Jun
1
comment Can Z/2 x Z/2 act freely on an infinite dimensional sphere?
Isn't $S^\infty$ homeomorphic to $S^\infty \times S^\infty$? That would answer your question. I think you can construct the map fairly explicitly, $S^n \times S^n \to S^{2n}$. You think of this map as crushing the two factors $S^n \times \{1\} \cup \{1\} \times S^n$ to a common point, with the map a homeomorphism otherwise. If you do this fairly naturally, this induces a map of the colimits $S^\infty \times S^\infty \to S^\infty$. This map is not a homeomorphism itself but it looks like it can be fixed as it fails to be a homeomorphism only by crushing two contractible subspaces.
Jun
1
reviewed Close Trying to relate the fundamental groupoid to vector bundles
Jun
1
comment Computation Time of Smith Normal Form in Maple
I don't know what algorithm Maple is using, but a 100x100 SNF computation, if the matrix is complicated or if the algorithm isn't very smart, can be a disaster. A sparse 120x120 matrix in a primitive SNF algorithm can lead to disaster. You can very easily go past a 64-bit integer size, or start swapping if you are using arbitrary-precision integers. Hafner-McCurley and Havas-Holt-Rees have fairly smart SNF algorithms that can easily handle 400x400 matrices on contemporary computers.
May
27
comment Injectivity of the Dehn-Nielsen-Baer map?
Correct. Things get complicated when your spaces have two or more non-trivial stages in their Postnikov towers.
May
27
comment How to give a $\Delta$-complex structure?
@TylerLawson: Perhaps I'm confused but I don't see how your concern is related to the original question. Are you interpreting the question as about ordered vs. unordered delta complexes?
May
27
comment Injectivity of the Dehn-Nielsen-Baer map?
The link between continuous maps of a $K(\pi,1)$ and homomorphisms of $\pi_1$ up to conjugation comes from obstruction theory. Given a homomorphism of $\pi_1$ you define a map between the $K(\pi,1)$ and itself, inducing the map on $\pi_1$, cellularly. You can extend the map to the entire space since it has no higher homotopy groups. I think there is a semi-detailed write up in Hatcher's algebraic topology book. The same kind of argument shows you any continuous map between $K(\pi,1)$ spaces is induced via this kind of construction.
May
27
comment How to give a $\Delta$-complex structure?
You need to check around every vertex there is a cycle of triangles, or if not a cycle, a linearly ordered set of triangles.
May
27
comment What's the detailed proof of “the composition of planar tangles is well-defined”?
Well in a sense we are dancing around a complete proof, but in part that's because the definition tries to avoid the technical issues at the heart of the problem. I think if you go through the argument that the group of isotopy-classes of diffeomorphisms of a pair $(S^1,F)$ where $F \subset S^1$ is finite, that this group is a dihedral group for an $n$-gon where $F$ has $n$ elements, once you see this proof you will likely see how it completes the proof you are looking for.
May
27
comment Example of a $G$-sphere that is not a $G$-representation sphere
@Zev: there are also examples of finite groups acting freely on spheres but the actions are not conjugate to linear actions. Do a Google search for "fake projective space" and you will find several papers. Generally people use this language in the manifold world rather than talking about $G$-spheres.
May
27
comment What's the detailed proof of “the composition of planar tangles is well-defined”?
With the labels you have just enough information to make the gluing. The key fact is, up to isotopy, there is a unique orientation-preserving diffeomorphism of a circle. But this is not true for relative diffeomorphisms of pairs (circle, finite subset). Diffeomorphisms of such objects are determined by not just whether or not they preserve orientation, but also where one point in the finite set is sent. That's the purpose of your "star" label, to determine where one point goes. Does this help?