Framed mapping class groups and strata of abelian differentials

via Zoom Video Conferencing: https://harvard.zoom.us/j/972495373

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.