Algebraic & Geometric Topology

Systoles and kissing numbers of finite area hyperbolic surfaces

Federica Fanoni and Hugo Parlier

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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.

Article information

Source
Algebr. Geom. Topol., Volume 15, Number 6 (2015), 3409-3433.

Dates
Received: 1 September 2014
Revised: 3 March 2015
Accepted: 7 April 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841072

Digital Object Identifier
doi:10.2140/agt.2015.15.3409

Mathematical Reviews number (MathSciNet)
MR3450766

Zentralblatt MATH identifier
1350.30064

Subjects
Primary: 30F10: Compact Riemann surfaces and uniformization [See also 14H15, 32G15]
Secondary: 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx] 53C22: Geodesics [See also 58E10]

Keywords
hyperbolic surfaces kissing numbers systoles

Citation

Fanoni, Federica; Parlier, Hugo. Systoles and kissing numbers of finite area hyperbolic surfaces. Algebr. Geom. Topol. 15 (2015), no. 6, 3409--3433. doi:10.2140/agt.2015.15.3409. https://projecteuclid.org/euclid.agt/1510841072


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