Classification of Rauzy classes in the moduli space of quadratic differentials

Corentin Boissy

Published 2009-04-24, updated 2013-05-16Version 2

We study relations between Rauzy classes coming from an interval exchange map and the corresponding connected components of strata of the moduli space of Abelian differentials. This gives a criterion to decide whether two permutations are in the same Rauzy class or not, without actually computing them. We prove a similar result for Rauzy classes corresponding to quadratic differentials.