Infinite translation surfaces with infinitely generated Veech groups
Pascal Hubert - LATP, case cour A, Faculté des sciences Saint Jérôme, Avenue Escadrille Normandie Niemen, 13397 Marseille cedex 20, France (email)
Abstract: We study infinite translation surfaces which are $\ZZ$-covers of finite square-tiled surfaces obtained by a certain two-slit cut and paste construction. We show that if the finite translation surface has a one-cylinder decomposition in some direction, then the Veech group of the infinite translation surface is either a lattice or an infinitely generated group of the first kind. The square-tiled surfaces of genus two with one zero provide examples for finite translation surfaces that fulfill the prerequisites of the theorem.
Keywords: Veech groups, infinite translation surfaces, holomorphic differentials.
Received: June 2010; Revised: September 2010; Published: January 2011.