Volume 10, issue 4 (2006)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Virtually Haken fillings and semi-bundles

Daryl Cooper and Genevieve S Walsh

Geometry & Topology 10 (2006) 2237–2245

arXiv: math.gt/0407328

Abstract

Suppose that M is a fibered three-manifold whose fiber is a surface of positive genus with one boundary component. Assume that M is not a semi-bundle. We show that infinitely many fillings of M along M are virtually Haken. It follows that infinitely many Dehn-surgeries of any non-trivial knot in the three-sphere are virtually Haken.

Keywords
virtually Haken conjecture, Dehn filling, semi-bundles
Mathematical Subject Classification 2000
Primary: 57M10
Secondary: 57M25
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Publication
Received: 23 September 2004
Revised: 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