## Geometry & Topology

### Virtual Betti numbers of genus 2 bundles

Joseph D Masters

#### Abstract

We show that if $M$ is a surface bundle over $S1$ with fiber of genus 2, then for any integer $n$, $M$ has a finite cover $M˜$ with $b1(M˜)>n$. A corollary is that $M$ can be geometrized using only the “non-fiber" case of Thurston’s Geometrization Theorem for Haken manifolds.

#### Article information

Source
Geom. Topol., Volume 6, Number 2 (2002), 541-562.

Dates
Revised: 9 August 2002
Accepted: 19 November 2002
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.gt/1513882934

Digital Object Identifier
doi:10.2140/gt.2002.6.541

Mathematical Reviews number (MathSciNet)
MR1941723

Zentralblatt MATH identifier
1009.57023

Subjects
Primary: 57M10: Covering spaces
Secondary: 57R10: Smoothing

#### Citation

Masters, Joseph D. Virtual Betti numbers of genus 2 bundles. Geom. Topol. 6 (2002), no. 2, 541--562. doi:10.2140/gt.2002.6.541. https://projecteuclid.org/euclid.gt/1513882934

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