Original scientific paper
https://doi.org/10.64785/mc.30.1.5
On the ends of groups and the Veech groups of infinite-genus surfaces
Camilo Ramírezm Maluendas
; camramirezma@unal.edu.co
Abstract
In this paper, we study the PSV construction, which provides a step by step method for obtaining tame translation surfaces with a suitable Veech group. In addition, we slightly modify this construction, and for each finitely generated subgroup \( G< GL_{+}(2, \mathbb{R})\) without contracting elements, we produce a tame translation surface S with infinite genus
such that its Veech group is G. Furthermore, the ends space of S can be written as B ⊔ U, where B is homeomorphic to the ends space of the group G, and U is a countable, discrete, dense, and open subset of the ends space of S.
Keywords
tame translation surface; Veech group; infinite-genus surface; PSV construction; ends of a group
Hrčak ID:
329424
URI
Publication date:
11.3.2025.
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