Vector fields, mapping class groups, and abelian differentials

Abstract:

The mapping class group of a surface is the set of its topological symmetries. Given a vector field on a surface, one would like to know which symmetries preserve (the isotopy class of) this vector field. Despite the fundamental nature of this question, little is known about these “framed mapping class groups.” In this talk I will describe some joint work with Nick Salter in which we gave explicit, finite generating sets for framed mapping class groups, as well as highlight an application to the topology of moduli spaces of abelian differentials