Dehn surgery, homology and hyperbolic volume

Agol, Ian; Culler, Marc; Shalen, Peter B

doi:10.2140/agt.2006.6.2297

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Editorial Interests

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author Index

To Appear

Other MSP Journals

Dehn surgery, homology and hyperbolic volume

Ian Agol, Marc Culler and Peter B Shalen

Algebraic & Geometric Topology 6 (2006) 2297–2312

DOI: 10.2140/agt.2006.6.2297

arXiv: math.GT/0508208

Abstract

If a closed, orientable hyperbolic $3$ –manifold $M$ has volume at most 1.22 then $H_{1} (M; ℤ_{p})$ has dimension at most $2$ for every prime $p \neq 2, 7$ , and $H_{1} (M; ℤ_{2})$ and $H_{1} (M; ℤ_{7})$ have dimension at most $3$ . The proof combines several deep results about hyperbolic $3$ –manifolds. The strategy is to compare the volume of a tube about a shortest closed geodesic $C \subset M$ with the volumes of tubes about short closed geodesics in a sequence of hyperbolic manifolds obtained from $M$ by Dehn surgeries on $C$ .

Keywords

hyperbolic manifold, volume, homology, drilling, Dehn surgery

Mathematical Subject Classification 2000

Primary: 57M50

Secondary: 57M27

References

Forward citations

Publication

Received: 14 July 2006

Accepted: 1 November 2006

Published: 8 December 2006

Authors

Ian Agol
Department of Mathematics, Statistics, and Computer Science (M/C 249) University of Illinois at Chicago 851 S Morgan St Chicago, IL 60607-7045 USA

Marc Culler
Department of Mathematics, Statistics, and Computer Science (M/C 249) University of Illinois at Chicago 851 S Morgan St Chicago, IL 60607-7045 USA

Peter B Shalen
Department of Mathematics, Statistics, and Computer Science (M/C 249) University of Illinois at Chicago 851 S Morgan St Chicago, IL 60607-7045 USA

Volume 6, issue 5 (2006)