Volume 8, issue 1 (2008)

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

Volume 18
Issue 4, 1883–2507
Issue 3, 1259–1881
Issue 2, 635–1258
Issue 1, 1–633

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
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Volume and homology of one-cusped hyperbolic $3$–manifolds

Marc Culler and Peter B Shalen

Algebraic & Geometric Topology 8 (2008) 343–379
Abstract

Let M be a complete, finite-volume, orientable hyperbolic manifold having exactly one cusp. If we assume that π1(M) has no subgroup isomorphic to a genus–2 surface group and that either (a) dimpH1(M; p) 5 for some prime p, or (b) dim2H1(M; 2) 4, and the subspace of H2(M; 2) spanned by the image of the cup product H1(M; 2) × H1(M; 2) H2(M; 2) has dimension at most 1, then volM > 5.06. If we assume that dim2H1(M; 2) 7 and that the compact core N of M contains a genus–2 closed incompressible surface, then volM > 5.06. Furthermore, if we assume only that dim2H1(M; 2) 7, then volM > 3.66.

Keywords
hyperbolic manifold, cusp, volume, homology, Dehn filling
Mathematical Subject Classification 2000
Primary: 57M50
Secondary: 57M27
References
Publication
Received: 24 August 2007
Revised: 3 February 2007
Accepted: 17 December 2007
Published: 12 May 2008
Authors
Marc Culler
Department of Mathematics (M/C 249)
University of Illinois at Chicago
851 S Morgan St
Chicago, IL 60607-7045
http://www.math.uic.edu/~culler
Peter B Shalen
Department of Mathematics (M/C 249)
University of Illinois at Chicago
851 S Morgan St
Chicago, IL 60607-7045
http://www.math.uic.edu/~shalen