Geometry & Topology

Virtual Betti numbers of genus 2 bundles

Joseph D Masters

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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

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

Received: 15 January 2002
Revised: 9 August 2002
Accepted: 19 November 2002
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

3–manifold geometrization virtual Betti number genus 2 surface bundle


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.

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