bio  website  math.berkeley.edu/~qchu 

location  Berkeley, CA  
age  24  
visits  member for  5 years, 7 months 
seen  24 mins ago  
stats  profile views  60,919 
I am a thirdyear graduate student at UC Berkeley. I'm interested in the interplay between homotopy theory, quantum field theory, manifold topology, and higher category theory.
11h

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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 finitedimensional (terrytao.wordpress.com/2011/05/24/…). 
1d

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Kgroups of a permutative category  are they finite?
What is the function of the strict associativity requirement here? 
1d

awarded  Nice Answer 
2d

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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. 
2d

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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 PeterWeyl 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

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real representation of a product group
@Jim: presumably $\mathbb{Z}_p$ refers to the cyclic group of order $p$, not the $p$adic integers. 
May 20 
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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 alloddcycles to allevencycles is described in the second paragraph, and its inverse is described in the third paragraph. 
May 20 
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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. 
May 20 
awarded  Nice Answer 
May 19 
answered  Permutations with all cycles odd length and permutations with all cycles even length 
May 19 
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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 
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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 
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Coxeter Isometry groups whose center has torsion
The center of a finite Coxeter group never contains an element of order $\ge 3$ (mhikari.com/imf/imf2013/29322013/…). 
May 19 
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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 
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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 
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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 
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projective module over C*algebra
@Liton: of course in that case $V$ and $W$ are isomorphic modules. 
May 18 
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projective module over C*algebra
@Yemon: I'm confused by your comment. Projectivity is a categorical property, and so it's invariant under automorphisms of the category of modules (and $\alpha$ induces such an automorphism). Or does projectivity mean something other than what I think it means in this context? 