Totally non congruence Veech groups

Abstract

Veech groups are discrete subgroups of SL(2, R) which play an important role in the theory of translation surfaces. For a special class of translation surfaces called origamis or square-tiled surfaces their Veech groups are subgroups of finite index of SL(2, Z). We show that each stratum of the space of translation surfaces contains infinitely many origamis whose Veech group is a totally non congruence group, i.e. it surjects to SL(2, Z/nZ) for any n.