Stokes matrices, character varieties, and points on spheres

Abstract: Moduli spaces of points on n-spheres carry natural actions of braid groups. For n=0,1, and 3, we prove that these symmetries extend to actions of mapping class groups of positive genus surfaces, through exceptional isomorphisms with certain character varieties. This relies on the existence of group structure for spheres in these dimensions. We also apply the exceptional isomorphisms to the study of Stokes matrices and exceptional collections of triangulated categories. Joint work with Junho Peter Whang.

Mathematics

Audience: researchers in the topic

ICCM 2020