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A McShane-type identity for closed surfaces

Part of: Abelian categories Topological manifolds Low-dimensional topology

Published online by Cambridge University Press:  11 January 2016

Yi Huang
Yi Huang*
Affiliation:
Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia, huay@ms.unimelb.edu.au
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Abstract.

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We prove a McShane-type identity: a series, expressed in terms of geodesic lengths, that sums to 2π for any closed hyperbolic surface with one distinguished point. To do so, we prove a generalized Birman-Series theorem showing that the set of complete geodesics on a hyperbolic surface with large cone angles is sparse.

MSC classification

Secondary: 57M50: Geometric structures on low-dimensional manifolds 57N05: Topology of $E^2$, $2$-manifolds 18E30: Derived categories, triangulated categories
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 219 , September 2015 , pp. 65 - 86
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2015

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