Systoles and kissing numbers of finite area hyperbolic surfaces

Fanoni, Federica; Parlier, Hugo

doi:10.2140/agt.2015.15.3409

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Systoles and kissing numbers of finite area hyperbolic surfaces

Federica Fanoni and Hugo Parlier

Algebraic & Geometric Topology 15 (2015) 3409–3433

DOI: 10.2140/agt.2015.15.3409

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

Volume 15, issue 6 (2015)