Virtual Betti numbers of genus 2 bundles

Masters, Joseph D¹

¹ Mathematics Department, Rice University, Houston, Texas 77005-1892, USA

Geometry & topology, Tome 6 (2002) no. 2, pp. 541-562.

Résumé

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 $b_1\left(\tilde{M}\right)>n$. A corollary is that $M$ can be geometrized using only the “non-fiber" case of Thurston’s Geometrization Theorem for Haken manifolds.

Détail

DOI : 10.2140/gt.2002.6.541

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

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