Volume 11, issue 3 (2011)

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

Volume 19
Issue 6, 2677–3215
Issue 5, 2151–2676
Issue 4, 1619–2150
Issue 3, 1079–1618
Issue 2, 533–1078
Issue 1, 1–532

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

Author Index
The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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