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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 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 2000
Primary: 57M10
Secondary: 57R10
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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
Joseph D Masters
Mathematics Department
Rice University
Houston
Texas 77005-1892
USA