Classification of Rauzy classes in the moduli space of quadratic differentials

TL;DR

This paper establishes criteria to determine if two permutations belong to the same Rauzy class in the moduli space of quadratic differentials, linking interval exchange maps and connected components without explicit computation.

Contribution

It extends the classification criteria for Rauzy classes from Abelian to quadratic differentials, providing a new method to identify class membership.

Findings

Criteria for Rauzy class membership without explicit computation

Connection between Rauzy classes and moduli space components

Extension of classification methods to quadratic differentials

Abstract

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.