Totally non-congruence Veech groups

Groups, geometry, and dynamics

article

Jan-Christoph Schlage-Puchta¹  Gabriela Weitze-Schmithüsen² 

[1] Universität Rostock;Universität des Saarlandes

关键词: Translation surfaces;    Veech groups;    congruence groups;   

DOI  :  10.4171/ggd/729

学科分类：神经科学

来源: European Mathematical Society

【 摘 要 】

Veech groups are discrete subgroups of SL(2,R)\mathrm{SL}(2,\mathbb{R})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)\mathrm{SL}(2,\mathbb{Z})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)\mathrm{SL} (2,\mathbb{Z}/n\mathbb{Z})SL(2,Z/nZ) for any nnn.

【 授权许可】

CC BY