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2018 Wild translation surfaces and infinite genus
Anja Randecker
Algebr. Geom. Topol. 18(5): 2661-2699 (2018). DOI: 10.2140/agt.2018.18.2661

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.

Citation

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Anja Randecker. "Wild translation surfaces and infinite genus." Algebr. Geom. Topol. 18 (5) 2661 - 2699, 2018. https://doi.org/10.2140/agt.2018.18.2661

Information

Received: 8 February 2017; Revised: 5 October 2017; Accepted: 11 March 2018; Published: 2018
First available in Project Euclid: 30 August 2018

zbMATH: 06935817
MathSciNet: MR3848396
Digital Object Identifier: 10.2140/agt.2018.18.2661

Subjects:
Primary: 53C10
Secondary: 37D50, 37E35, 57M50

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 5 • 2018
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