Betti numbers of unordered configuration spaces of a punctured torus

Yifeng Huang
University of Michigan
Friday, September 18, 2020 - 3:35pm to 4:35pm
Zoom ID is 941-2794-9847

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\neq x_j for i\neq 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.   See seminar website for password: http://www-users.math.umn.edu/~ovenh001/seminar.html