Volume 11, issue 3 (2011)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 25, 1 issue

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Systoles of hyperbolic manifolds

Mikhail V Belolipetsky and Scott A Thomson

Algebraic & Geometric Topology 11 (2011) 1455–1469
Abstract

We show that for every n 2 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 n 3 the volumes of these manifolds grow at least as 1ϵn2 when ϵ 0.

Keywords
systole, hyperbolic manifold, nonarithmetic lattice
Mathematical Subject Classification 2010
Primary: 22E40, 53C22
References
Publication
Received: 4 October 2010
Revised: 24 January 2011
Accepted: 12 February 2011
Published: 17 May 2011
Authors
Mikhail V Belolipetsky
Department of Mathematical Sciences
Durham University
South Road
Durham
DH1 3LE
United Kingdom
Institute of Mathematics
Koptyuga 4
630090 Novosibirsk
Russia
Scott A Thomson
Department of Mathematical Sciences
Durham University
South Road
Durham
DH1 3LE
United Kingdom