Origamis with non congruence Veech groups

Details Origamis with non congruence Veech groups Origamis with non congruence Veech groups

2007-04-03

arxiv.org/abs/0704.0416v1

Proceedings of 34th Symposium on Transformation Groups, Edited by T. Kawakami, Wing Co., Ltd., 2007 (p.31 - 55).

Mathematics

Geometric Topology

25 pages

Scientific paper

As main result we show that for each g > 1 there is some translation surface of genus g whose Veech group is a non congruence subgroup of SL(2,Z). We use origamis/square-tiled surfaces to produce our examples. The article is divided into two parts: In the first part we introduce translation surfaces, origamis, Veech groups and Teichmueller curves and show for two origamis in genus 2 that their Veech groups are non congruence groups; in the second part we provide a technique that produces sequences of origamis whose Veech groups are decreasing. This is used to prove the main result.

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