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.
Highlights
Rauzy induction was first introduced as a tool to study the dynamics of interval exchange transformations [Rau79]
A Rauzy class is a minimal subset of irreducible permutations which is invariant by the two combinatorial operations associated to the Rauzy induction
The Veech construction enables us to associate to a Rauzy class a connected component of the moduli space of Abelian differentials with prescribed singularities
Summary
Rauzy induction was first introduced as a tool to study the dynamics of interval exchange transformations [Rau79]. The Veech construction enables us to associate to a Rauzy class a connected component of the moduli space of Abelian differentials with prescribed singularities. This will correspond to Proposition 4.1 for Abelian differential and Proposition 4.4 for quadratic differentials.
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