Monodromy kernels for strata of translation surfaces

Riccardo Giannini (University of Glasgow)

Monday 17th February 16:00-17:00 Maths 311B

Abstract

Translation surfaces are closed Riemann surfaces with a flat metric on the complement of some finite number of points, around which the metric is given by cyclically glueing a finite number of half-planes. Their moduli spaces can be stratified in orbifolds, and there are connected components consisting of hyperelliptic Riemann surfaces that are topologically well-understood. However, studying the topology of the non-hyperelliptic components proves to be more intricate. For example, it has been conjectured that their (orbifold) fundamental groups are commensurable with some mapping class groups, but it is not known whether or not the natural monodromy map of a non-hyperelliptic component is an isomorphism onto its image. In this talk, we are going to show why the kernel of some monodromies in low genera are very large, as they contain a non-abelian free group of rank 2. The result suggests that in some cases the commensurability class of these orbifold fundamental group might not coincide with any sort of mapping class group.

Add to your calendar

Download event information as iCalendar file (only this event)