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2011 Systoles of hyperbolic manifolds
Mikhail V Belolipetsky, Scott A Thomson
Algebr. Geom. Topol. 11(3): 1455-1469 (2011). DOI: 10.2140/agt.2011.11.1455

Abstract

We show that for every n2 and any ϵ>0 there exists a compact hyperbolic n–manifold with a closed geodesic of length less than ϵ. When ϵ is sufficiently small these manifolds are non-arithmetic, and they are obtained by a generalised inbreeding construction which was first suggested by Agol for n=4. We also show that for n3 the volumes of these manifolds grow at least as 1ϵn2 when ϵ0.

Citation

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Mikhail V Belolipetsky. Scott A Thomson. "Systoles of hyperbolic manifolds." Algebr. Geom. Topol. 11 (3) 1455 - 1469, 2011. https://doi.org/10.2140/agt.2011.11.1455

Information

Received: 4 October 2010; Revised: 24 January 2011; Accepted: 12 February 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1248.22004
MathSciNet: MR2821431
Digital Object Identifier: 10.2140/agt.2011.11.1455

Subjects:
Primary: 22E40, 53C22

Rights: Copyright © 2011 Mathematical Sciences Publishers

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