Veech groups of infinite genus surfaces

2016/03/01 by Camilo Ramirez Maluendas, Maluendas, Camilo Ramirez, Ferran Valdez +1
Mathematics · #20F65 #53A99 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:20F65 #msc:53A99

paper · pdf · doi:10.48550/arxiv.1603.00503

26 pages, 12 figures

arxiv created 2016/03/01 · arxiv updated 2016/03/03

Abstract

We show that every countable subgroup G<\rm GL₊(2,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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