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Classification of Rauzy classes in the moduli space of abelian and quadratic differentials. (English) Zbl 1268.37039

Summary: 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.

MSC:

37E05 Dynamical systems involving maps of the interval
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
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