50,141 reputation
15190451
bio website math.berkeley.edu/~qchu
location Berkeley, CA
age 24
visits member for 5 years, 7 months
seen 25 mins ago

I am a third-year graduate student at UC Berkeley. I'm interested in the interplay between homotopy theory, quantum field theory, manifold topology, and higher category theory.


5h
comment Is the space of smooth maps $C^{\infty}(M,N)$ with the Whitney $C^{\infty}$ topology locally compact, if $M$ is compact
Take $N = \mathbb{R}$. Then a locally compact Hausdorff topological vector space is necessarily finite-dimensional (terrytao.wordpress.com/2011/05/24/…).
18h
comment K-groups of a permutative category - are they finite?
What is the function of the strict associativity requirement here?
19h
comment A question and a conjecture on $USp(N)$ group
Crossposted (please don't do this): math.stackexchange.com/questions/1293679/…
1d
awarded  Nice Answer
1d
comment real representation of a product group
It's certainly true that the more interesting stuff leverages connectedness heavily, in the same way that, to pick a random example, the more interesting parts of algebraic topology leverage CW complexes heavily. But that doesn't mean that a finite group isn't a compact Lie group, any more than it means that the Cantor set isn't a topological space.
1d
comment real representation of a product group
@Jim: I don't understand your objection. To the extent that the simplest aspects of the representation theory of compact Lie groups (namely complete reducibility and the Peter-Weyl theorem) don't depend on connectedness, they apply equally well to finite groups, and it's a natural level of generality to work at if you want the first statement the OP wrote down to be true (that irreps of a product of two groups correspond to tensor products of irreps).
2d
comment real representation of a product group
@Jim: presumably $\mathbb{Z}_p$ refers to the cyclic group of order $p$, not the $p$-adic integers.
2d
comment Permutations with all cycles odd length and permutations with all cycles even length
@Jon: I don't understand that comment. I've provided an explicit bijection: the map from all-odd-cycles to all-even-cycles is described in the second paragraph, and its inverse is described in the third paragraph.
2d
comment Permutations with all cycles odd length and permutations with all cycles even length
@Jon: both directions of the bijection cause every cycle to change in size by $\pm 1$, which sends odd cycles to even cycles and vice versa. And as David says, this is a different argument from the argument about partitions.
2d
awarded  Nice Answer
May
19
answered Permutations with all cycles odd length and permutations with all cycles even length
May
19
comment Coxeter Isometry groups whose center has torsion
@Tom: it was just the first reference I could find. Googling is faster than looking things up in Humphreys...
May
19
comment When are configuration spaces aspherical?
Incidentally, whether you require boundaryless or not is irrelevant; configuration spaces on a manifold with boundary are homotopy equivalent to configuration spaces on the interior.
May
19
revised When are configuration spaces aspherical?
added 2 characters in body
May
19
answered When are configuration spaces aspherical?
May
19
comment Coxeter Isometry groups whose center has torsion
The center of a finite Coxeter group never contains an element of order $\ge 3$ (m-hikari.com/imf/imf-2013/29-32-2013/…).
May
19
comment Intrinsic definition of arc length
@Felix: you do not need a parameterization. Provided that you know where the two endpoints are, you can take the limit (in the sense of nets) over all PL approximations with the same endpoints. That just requires that you know where the points on the curve are.
May
18
comment real representation of a product group
Do you know how to deduce the classification of irreducible real representations from the classification of irreducible complex representations?
May
18
comment projective module over C*-algebra
@Yemon: they are not necessarily isomorphic. But they are related by an automorphism of the category of modules (again, unless the definitions here are not what I think they are), so any categorical property that one has, the other must also have.
May
18
comment projective module over C*-algebra
@Liton: of course in that case $V$ and $W$ are isomorphic modules.