Virtually Haken fillings and semi-bundles

Cooper, Daryl; Walsh, Genevieve S

doi:10.2140/gt.2006.10.2237

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Virtually Haken fillings and semi-bundles

Daryl Cooper and Genevieve S Walsh

Geometry & Topology 10 (2006) 2237–2245

DOI: 10.2140/gt.2006.10.2237

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 $\partial M$ 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

Volume 10, issue 4 (2006)