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Article

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).