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Algebra Seminar

Betti numbers of unordered configuration spaces of a punctured torus

Yifeng Huang, (U. Michigan)

Date & time: Wednesday, 23 September 2020 at 2:00PM - 3:00PM

Let X be a elliptic curve over C with one point removed, and consider the unordered configuration spaces Conf^n(X)={(x_1,...,x_n): x_i e x_j for i e j} / S_n.  We present a rational function in two variables from whose coefficients we can read off the i-th Betti numbers of Conf^n(X) for all i and n. The key of the proof is a property called "purity", which was known to Kim for (ordered or unordered) configuration spaces of the complex plane with r >= 0 points removed. We show that the unordered configuration spaces of X also have purity (but with different weights). This is a joint work with G. Cheong.

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