bio | website | math.rice.edu/~andyp |
---|---|---|
location | Houston, TX | |
age | 34 | |
visits | member for | 4 years, 6 months |
seen | 4 hours ago | |
stats | profile views | 12,365 |
associate professor at Rice University
Apr 14 |
comment |
What are the areas of modern math?
@Sebastian : This site is intended for "research-level mathematicians", which for the most part means PhD students and professors of mathematics (and other people with similar backgrounds). If this is not your background (and if you find the questions and answers here completely opaque, then it likely is not), then you would probably be happier at math.stackexchange.com, which is open to people at all levels. |
Apr 12 |
comment |
Eilenberg-MacLane Spaces of “large” groups
These are more natural things to consider than the comments seem to indicate. For a reasonable topological group $G$, the space $BG$ classifies principal $G$-bundles, while the space $BG^{\delta}$ classifies flat principal $G$-bundles (here $G^{\delta}$ is $G$ considered as a discrete group). So the cohomology of $BG^{\delta}$ consists of characteristic classes for flat bundles; obviously these of great interest. |
Apr 12 |
comment |
Eilenberg-MacLane Spaces of “large” groups
The conjecture in this paper has recently been proved in most cases by F. Morel; see Corollary 2 of mathematik.uni-muenchen.de/~morel/FriedlanderMilnorNew.pdf |
Apr 11 |
comment |
Mean Value Theorem Question
MO is not for homework and is intended for questions at the PhD level and above. I've voted to close. |
Apr 7 |
answered | On trivalent spines of surfaces |
Apr 2 |
comment |
Are the mapping class groups of manifolds finitely presentable?
@DannyRuberman : Cool, I didn't know about that paper. Thanks! |
Mar 29 |
awarded | Enlightened |
Mar 29 |
awarded | Nice Answer |
Mar 29 |
comment |
Are the mapping class groups of manifolds finitely presentable?
Nothing is known in dimension $4$. In dimension $3$, they are always finitely presentable. This is very explicit for prime $3$-manifolds. For instance, the mapping class groups of hyperbolic $3$-manifolds are finite by Mostow rigidity, and one can show that the mapping class groups of Seifert fibered spaces are closely connected to the mapping class groups of their base surfaces. For non-prime $3$-manifolds, things are a little more complicated. Hatcher's survey mentioned in my answer has a good description of all of this. |
Mar 29 |
revised |
Are the mapping class groups of manifolds finitely presentable?
added 745 characters in body |
Mar 29 |
answered | Are the mapping class groups of manifolds finitely presentable? |
Mar 25 |
answered | kernel of monodromy action of braid group on homology of hyperelliptic curve |
Mar 14 |
comment |
References about 3-manifolds
A lesser known source is Fomenko-Matveev's book "Algorithmic and computer methods for three-manifolds". Despite its title, it has nothing to do with computers, but instead is a very nice basic course on 3-manifold topology. The pictures in it are really wonderful. |
Mar 4 |
comment |
Does the centroid depend continuously on the curve?
@LiviuNicolaescu : I think that Paul is thinking of $\gamma$ as a map from $[0,1]$ to $\mathbb{R}^n$. |
Feb 24 |
comment |
Modifying Dehn's algorithm to allow equal length replacements?
Remark : A group $G$ has a presentation for which there is a classical Dehn algorithm if and only if $G$ is hyperbolic. You indicated that you know the "if" direction; for the "only if" direction, it is clear that if there is a presentation where the classical Dehn algorithm works, then the group has a linear Dehn function (which is known to be equivalent to hyperbolicity). |
Feb 20 |
comment |
How do you prove that a subset of L is regular is L is regular?
MO is intended for topics at the mathematics PhD student level and above. I have voted to close. |
Feb 20 |
answered | (Un)distorted subgroups in the mapping class group: reference required. |
Feb 18 |
comment |
Natural constructions (not depending on parameters)
I think that Pete's comment describes the issues with this question perfectly. And I'm sorry if you feel like we demand patience here, but that is the generally agreed upon policy. If you don't get a good answer on math.se, you should think about how to improve your question to get one rather than just copying it here. |
Feb 18 |
comment |
Natural constructions (not depending on parameters)
I'm not sure this is an appropriate question for MO, but even if it is you only waited 24 hours to get an answer on math.SE. You should wait at least a couple of weeks. |
Feb 17 |
comment |
Singular chains generated by manifolds with corners — does it really work?
I think I spoke too fast when I wrote that one can following the usual proof word-for-word; I had quickly gone through it and didn't see any obstructions, but you're right that it's not so clear. But if it's true, then surely that's the way to go about proving it. |