Volume 18, issue 5 (2018)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Wild translation surfaces and infinite genus

Anja Randecker

Algebraic & Geometric Topology 18 (2018) 2661–2699
Abstract

The Gauss–Bonnet formula for classical translation surfaces relates the cone angle of the singularities (geometry) to the genus of the surface (topology). When considering more general translation surfaces, we observe so-called wild singularities for which the notion of cone angle is not applicable any more.

We study whether there still exist relations between the geometry and the topology for translation surfaces with wild singularities. By considering short saddle connections, we determine under which conditions the existence of a wild singularity implies infinite genus. We apply this to show that parabolic or essentially finite translation surfaces with wild singularities have infinite genus.

Keywords
translation surfaces, wild singularities, infinite topological type
Mathematical Subject Classification 2010
Primary: 53C10
Secondary: 37D50, 37E35, 57M50
References
Publication
Received: 8 February 2017
Revised: 5 October 2017
Accepted: 11 March 2018
Published: 22 August 2018
Authors
Anja Randecker
Department of Mathematics
University of Toronto
Toronto, ON
Canada
http://www.math.toronto.edu/anja/