Boissy, Corentin Classification of Rauzy classes in the moduli space of abelian and quadratic differentials. (English) Zbl 1268.37039 Discrete Contin. Dyn. Syst. 32, No. 10, 3433-3457 (2012). 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. Cited in 8 Documents 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) Keywords:interval exchange maps; linear involutions; Rauzy classes; quadratic differentials; moduli spaces PDFBibTeX XMLCite \textit{C. Boissy}, Discrete Contin. Dyn. Syst. 32, No. 10, 3433--3457 (2012; Zbl 1268.37039) Full Text: DOI arXiv