Volume 10, issue 4 (2006)

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

Volume 21
Issue 6, 3191–3810
Issue 5, 2557–3190
Issue 4, 1931–2555
Issue 3, 1285–1930
Issue 2, 647–1283
Issue 1, 1–645

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Three-manifolds, virtual homology, and group determinants

Daryl Cooper and Genevieve S Walsh

Geometry & Topology 10 (2006) 2247–2269

arXiv: math.GT/0603152

Abstract

We apply representation theory to study the homology of equivariant Dehn-fillings of a given finite, regular cover of a compact 3–manifold with boundary a torus. This yields a polynomial which gives the rank of the part of the homology carried by the solid tori used for Dehn-filling. The polynomial is a symmetrized form of the group determinant studied by Frobenius and Dedekind. As a corollary every such hyperbolic 3–manifold has infinitely many virtually Haken Dehn-fillings.

Keywords
Group determinant, Dehn-filling, virtually Haken
Mathematical Subject Classification 2000
Primary: 57M10
Secondary: 57M25, 20C10
References
Forward citations
Publication
Received: 8 March 2006
Accepted: 24 October 2006
Published: 29 November 2006
Proposed: David Gabai
Seconded: Cameron Gordon, Joan Birman
Authors
Daryl Cooper
Math Department
UCSB
Santa Barbara, CA 93106
USA
Genevieve S Walsh
Department of Math
Tufts University
Medford, MA 02155
USA
and
Département de Mathématiques
UQAM
Montréal, QC H3C 3J7
Canada