Substitutions and cutting sequences for Bouw Moeller Veech surfaces
speaker: Corinna Ulcigrai (University of Bristol)abstract: The cutting sequence of a linear trajectory on a translation surface encodes the sequence of labels of sides of a polygonal presentation of the surface which are hit by the trajectory. In the case of a torus, cutting sequences of linear trajectories in a square coincide with the well known Sturmian sequences and can be characterized as limit of products of two substitutions, a characterization known as S-adic. We gave a similar characterization for cutting sequences on the octagon and regular 2n-gons in joint work with J. Smillie. We consider here the family of Veech translation surfaces discovered by Bouw-Moeller surfaces, obtained (as described by Hooper) by glueing a collection of semi-regular polygons. We provide for these sequences a full S-adic characterization governed by a continued fraction-like map. As for the square and 2n-gons, we exploit renormalization and a combinatorial notion of derivation. One of the novelties is that we do not use directly Veech group element and we crucially exploit as a technnical tool Hooper diagrams. This is joint work with Diana Davis and Irene Pasquinelli.
timetable:
Mon 4 Apr, 10:00 - 11:00, Aula Dini
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