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Systoles and kissing numbers of finite area hyperbolic surfaces (1408.6048v2)
Published 26 Aug 2014 in math.GT and math.DG
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.
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