On the Ends of groups and the Veech groups of infinite-genus surfaces

Camilo Ramírez Maluendas

Vol. 30 No. 1 (2025)

Regular Articles

On the Ends of groups and the Veech groups of infinite-genus surfaces

Published 2025-03-11

Camilo Ramírez Maluendas

Camilo Ramírez Maluendas
Departamento de Matemática y Estadística, Universidad Nacional de Colombia, Sede Manizales

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Abstract

In this paper we study the PSV construction, which describes a step by step to obtain tame translation surfaces with suitable Veech group. Moreover, we modify slightly such construction and obtain for each finitely generated subgroup $G<{\rm GL}_{+}(2,\mathbb{R})$ without contracting elements, a tame translation surface $S$ with infinite genus, such that its Veech group is $G$, and the ends space of $S$ can be written as ${\rm Ends}(G)\sqcup \mathcal{U}$, where ${\rm Ends}(G)$ is the end space of the group $G$, and $\mathcal{U}$ is a countable discrete dense open subset of the ends space of $S$.

Keywords

Tame translation surface, Veech group, Infinite-genus surface, PSV construction, ends of a group

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Supplementary File(s)

5099-15365-1-SP - final