Veech groups of infinite genus surfaces

Camilo Ramirez Maluendas; Ferran Valdez

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arXiv · 1603.00503

Veech groups of infinite genus surfaces

Camilo Ramirez Maluendas·Ferran Valdez

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Abstract

We show that every countable subgroup $G<\rm GL_+(2,\mathbb{R})$ without contracting elements is the Veech group of a tame translation surface $S$ of infinite genus, for infinitely many different topological types of $S$. Moreover, we prove that as long as every end has genus, there are no restrictions on the topological type of $S$ to realise all possible uncountable Veech groups.

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Camilo Ramirez Maluendas, Ferran Valdez. 2016-03-01. Veech groups of infinite genus surfaces. https://arxiv.org/abs/1603.00503

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