Relations in cohomology rings via mirror symmetry

Abstract: I will talk about Lefschets-type sl2 action on the cohomology of the moduli space of stable GL_n-Higgs bundles. It turns out, the S matrix of this action interchanges the operators of multiplication by certain tautological classes with certain monodromy operators. In a joint project with Tamas Hausel we attempt to guess a complete list of relations between these operators. This is then implies some relations in the cohomology ring. Conjecturally, we obtain all relations in ranks 2 and 3.

Mathematics

Audience: researchers in the topic

SMSMS 2021 (School on Mirror Symmetry and Moduli Spaces)