Totally non-congruence Veech groups

  • Jan-Christoph Schlage-Puchta

    Universität Rostock, Germany
  • Gabriela Weitze-Schmithüsen

    Universität des Saarlandes, Saarbrücken, Germany
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Veech groups are discrete subgroups of 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 . 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 for any .

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Jan-Christoph Schlage-Puchta, Gabriela Weitze-Schmithüsen, Totally non-congruence Veech groups. Groups Geom. Dyn. 17 (2023), no. 3, pp. 1115–1131

DOI 10.4171/GGD/729