Congruence Veech groups

Abstract

We study Veech groups of covering surfaces of primitive translation surfaces. Therefore we define congruence subgroups in Veech groups of primitive translation surfaces using their action on the homology with entries in Z/aZ. We introduce a congruence level definition and a property of a primitive translation surface which we call property (★). It guarantees that partition stabilising congruence subgroups of this level occur as Veech groups of a translation covering.