Volume 17, issue 1 (2017)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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+(2, ) 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
References
Publication
Received: 26 April 2016
Revised: 1 June 2016
Accepted: 16 June 2016
Published: 26 January 2017
Authors
Camilo Ramírez Maluendas
Fundación Universitaria Konrad Lorenz
Carrero 9 bis #62-43
Bogotá
Colombia
http://docentes.konradlorenz.edu.co/2015/06/camilo-ramirez-maluendas.html
Ferrán Valdez
Center of Mathematical Sciences
National Autonomous University of Mexico (UNAM)
Campus Morelia
C.P. 58190
Morelia
Mexico
http://www.matmor.unam.mx/~ferran/