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 moduli of local systems. 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.