Totally non congruence Veech groups

2018/02/14 by Jan‐Christoph Schlage‐Puchta, Schlage-Puchta, Jan-Christoph, Gabriela Weitze-Schmithuesen +1
Computer Science · Engineering · Mathematics · #14H30 #20F28 #32G15 #53C10 #Advanced Materials and Mechanics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1802.05024

openalex publication_date 2018/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

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• A characterization of Veech groups in terms of origamis
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