Realizing groups as symmetries of infinite translation surfaces

Autor:	Artigiani, Mauro, Randecker, Anja, Sadanand, Chandrika, Valdez, Ferrán, Weitze-Schmithüsen, Gabriela
Rok vydání:	2023
Předmět:	Mathematics - Geometric Topology Mathematics - Group Theory 57M60 (Primary) 30F99 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We provide a complete classification of groups that can be realized as isometry groups of a translation surface $M$ with non-finitely generated fundamental group and no planar ends. Furthermore, we demonstrate that if $S$ has no non-displaceable subsurfaces and its space of ends is self-similar, then every countable subgroup of $\operatorname{GL}^+(2,\mathbb{R})$ can be realized as the Veech group of a translation surface $M$ homeomorphic to $S$. The latter result generalizes and improves upon the previous findings of Przytycki-Valdez-Weitze-Schmith\"{u}sen and Maluendas-Valdez. To prove these results, we adapt ideas from the work of Aougab-Patel-Vlamis, which focused on hyperbolic surfaces, to translation surfaces. Comment: 25 pages, 7 figures, comments are welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2311.00158 Zobrazit plný text záznamu View this record from Arxiv