Geometry & Topology 6 (2002) 541–562

DOI: 10.2140/gt.2002.6.541

arXiv: math.GT/0201118

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.

Keywords

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

Mathematical Subject Classification

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