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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Systoles and kissing numbers of finite area hyperbolic surfaces

Federica Fanoni and Hugo Parlier

Algebraic & Geometric Topology 15 (2015) 3409–3433
Abstract

We study the number and the length of systoles on complete finite area orientable hyperbolic surfaces. In particular, we prove upper bounds on the number of systoles that a surface can have (the so-called kissing number for hyperbolic surfaces). Our main result is a bound which only depends on the topology of the surface and which grows subquadratically in the genus.

Keywords
hyperbolic surfaces, kissing numbers, systoles
Mathematical Subject Classification 2010
Primary: 30F10
Secondary: 32G15, 53C22
References
Publication
Received: 1 September 2014
Revised: 3 March 2015
Accepted: 7 April 2015
Published: 12 January 2016
Authors
Federica Fanoni
Mathematics Institute
Zeeman Building
University of Warwick
Coventry CV4 7AL
UK
Hugo Parlier
Department of Mathematics
University of Fribourg
Ch. du Musée 23
CH-1700 Fribourg
Switzerland