#### Volume 6, issue 2 (2002)

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Virtual Betti numbers of genus 2 bundles

### Joseph D Masters

Geometry & Topology 6 (2002) 541–562
 arXiv: math.GT/0201118
##### Abstract

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 $\stackrel{˜}{M}$ with ${b}_{1}\left(\stackrel{˜}{M}\right)>n$. 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
Primary: 57M10
Secondary: 57R10