Virtual Betti numbers of genus 2 bundles

We show that if $M$ is a surface bundle over $S^{1}$ with fiber of genus 2, then for any integer $n$ , $M$ has a finite cover $\tilde{M}$ with $b_{1} (\tilde{M}) > n$ . A corollary is that $M$ can be geometrized using only the “non-fiber" case of Thurston’s Geometrization Theorem for Haken manifolds.

Keywords

3–manifold, geometrization, virtual Betti number, genus 2 surface bundle

Mathematical Subject Classification 2000

Primary: 57M10

Secondary: 57R10

References

Forward citations

Publication

Received: 15 January 2002

Revised: 9 August 2002

Accepted: 19 November 2002

Published: 24 November 2002

Proposed: Walter Neumann

Seconded: Cameron Gordon, Joan Birman

Authors

Joseph D Masters
Mathematics Department Rice University Houston Texas 77005-1892 USA

Volume 6, issue 2 (2002)

Joseph D Masters