Framed mapping class groups and strata of abelian differentials

Abstract: Strata of abelian differentials have long been of interest for their dynamical and algebro-geometric properties, but relatively little is understood about their topology. I will describe a project aimed at understanding the (orbifold) fundamental groups of non-hyperelliptic stratum components. The centerpiece of this is the monodromy representation valued in the mapping class group of the surface relative to the zeroes of the differential. For $g \ge 5$, we give a complete description of this as the stabilizer of the framing of the (punctured) surface arising from the flat structure associated to the differential. This is joint work with Aaron Calderon.

complex variablesdynamical systems

Audience: researchers in the topic

Informal geometry and dynamics seminar