#### Volume 17, issue 1 (2017)

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Veech groups of infinite-genus surfaces

### Camilo Ramírez Maluendas and Ferrán Valdez

Algebraic & Geometric Topology 17 (2017) 529–560
##### Abstract

We show that every countable subgroup $G<{GL}_{+}\left(2,ℝ\right)$ 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 realize all possible uncountable Veech groups.

##### Keywords
infinite type translation surface, Veech group
##### Mathematical Subject Classification 2010
Primary: 20F65, 53A99