Volume 14, issue 3 (2014)

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

Volume 19
Issue 7, 3217–3753
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 and Dehn surgery for hyperbolic $3$–manifolds

Grant S Lakeland and Christopher J Leininger

Algebraic & Geometric Topology 14 (2014) 1441–1460
Abstract

Given a closed hyperbolic 3–manifold M of volume V , and a link L M such that the complement M L is hyperbolic, we establish a bound for the systole length of M L in terms of V . This extends a result of Adams and Reid, who showed that in the case that M is not hyperbolic, there is a universal bound of 7.35534 As part of the proof, we establish a bound for the systole length of a noncompact finite volume hyperbolic manifold which grows asymptotically like 4 3 logV .

Keywords
systole, Kleinian group, isometric sphere
Mathematical Subject Classification 2010
Primary: 57M50
References
Publication
Received: 15 July 2013
Revised: 29 October 2013
Accepted: 5 November 2013
Published: 7 April 2014
Authors
Grant S Lakeland
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W Green St
273 Altgeld Hall
Urbana, IL 61801
USA
Christopher J Leininger
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W Green St
273 Altgeld Hall
Urbana, IL 61801
USA