Geodesic
Totally non-congruence Veech groups
Jan-Christoph Schlage-Puchta1 ; Gabriela Weitze-Schmithüsen2
1Universität Rostock, Germany
2Universität des Saarlandes, Saarbrücken, Germany
Groups, geometry, and dynamics, Tome 17 (2023) no. 3, pp. 1115-1131

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DOI

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.
DOI : 10.4171/ggd/729
Classification : 14-XX, 32-XX, 53-XX
Mots-clés : Translation surfaces, Veech groups, congruence groups

Jan-Christoph Schlage-Puchta  1   ; Gabriela Weitze-Schmithüsen  2

1 Universität Rostock, Germany
2 Universität des Saarlandes, Saarbrücken, Germany 
Jan-Christoph Schlage-Puchta; Gabriela Weitze-Schmithüsen. Totally non-congruence Veech groups. Groups, geometry, and dynamics, Tome 17 (2023) no. 3, pp. 1115-1131. doi: 10.4171/ggd/729
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     title = {Totally non-congruence {Veech} groups},
     journal = {Groups, geometry, and dynamics},
     pages = {1115--1131},
     year = {2023},
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     number = {3},
     doi = {10.4171/ggd/729},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/729/}
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