## Origamis with non congruence Veech groups

** Gabriela Schmithuesen**

*In Proceedings of Symposium on Transformation Groups, Yokohama, November 2006.*

This article is divided into two parts. In the first part we give an introduction to origamis (often also called

square-tiled surfaces) and their Veech groups.

In the second part we give two examples of origamis in genus two whose Veech groups are non congruence subgroups of SL(2,Z). We find a construction how to build infinite sequences of origamis all of them having a Veech group which is a non congruence group. We prove as main theorem that in each genus there exist origamis, whose Veech groups are non congruence subgroups of SL(2,Z).