#### Volume 10, issue 4 (2006)

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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 $\partial M$ 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
Primary: 57M10
Secondary: 57M25
##### 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