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bio website math.berkeley.edu/~qchu
location Berkeley, CA
age 24
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I'm a third-year graduate student in pure mathematics at UC Berkeley. You can contact me at qchu[at]math[dot]berkeley[dot]edu.


1h
awarded  Nice Question
3h
answered Is there any relationship between the Euler class and the Vandermonde determinant?
1d
comment How to extend index theorem to infinite dimensional manifolds?
I don't really know what you have in mind on the analysis side. The index-theoretic description of the Euler characteristic involves constructing, one way or another, the Euler class of a compact oriented manifold, which lives in top cohomology. Where could the Euler class possibly live on an infinite-dimensional manifold?
1d
comment How to extend index theorem to infinite dimensional manifolds?
The Euler characteristic of a contractible space is (perfectly well-defined and equal to) $1$, not $0$. Roughly speaking the problem here is a failure of monotone convergence (thinking of the Euler characteristic as a kind of measure): the spheres only have homology in two places and when passing to the limit above, the homology in the top-dimensional place has escaped off to infinity. That's nothing too unexpected.
2d
answered Take contraction wrt a vector field twice and define kernel mod image. Does that give anything interesting?
2d
comment Quotient of the hyperbolic plane with respect to commutator group of $\pi_1(\Sigma_g)$
I would run that argument the other way: $\mathbb{H}/[G, G]$ is an infinite covering space of $\Sigma_g$, hence it is noncompact. As a noncompact surface, it's homotopy equivalent to a $1$-dimensional CW complex, hence its fundamental group is free.
2d
awarded  Nice Answer
Oct
17
awarded  Excavator
Oct
17
revised Wonderful applications of the Vandermonde determinant
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Oct
17
awarded  Popular Question
Oct
15
asked Is there any relationship between the Euler class and the Vandermonde determinant?
Oct
15
comment “extended TQFT” versus “TQFT with defects”
I think you want the cobordism hypothesis with singularities (Theorem 4.3.11 in arxiv.org/abs/0905.0465).
Oct
13
awarded  Yearling
Oct
8
revised Why the Dold-Thom theorem?
edited body
Oct
8
revised Why the Dold-Thom theorem?
added 681 characters in body
Oct
8
revised Why the Dold-Thom theorem?
deleted 12 characters in body
Oct
8
answered Why the Dold-Thom theorem?
Oct
7
awarded  Necromancer
Oct
6
comment Classifying space for fibrations with Eilenberg-MacLane space as fibers
What's true with no hypotheses on the base is that $[B, K(\pi, n+1)]$ classifies principal $K(\pi, n)$-fibrations.
Oct
6
comment From the perspective of bordism categories, where does the ring structure on Thom spectra come from?
@Thomas: yes, but my comment above is not about the cartesian product of manifolds. It is about the cartesian product in $\text{Bord}$.