Geometry & Topology, Vol. 6 (2002) Paper no. 19, pages 541--562.

Virtual Betti numbers of genus 2 bundles

Joseph D Masters

Abstract. 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(tilde(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

AMS subject classification. Primary: 57M10. Secondary: 57R10.

DOI: 10.2140/gt.2002.6.541

E-print: arXiv:math.GT/0201118

Submitted to GT on 15 January 2002. (Revised 9 August 2002.) Paper accepted 19 November 2002. Paper published 24 November 2002.

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Joseph D Masters
Mathematics Department, Rice University
Houston, TX 77005-1892, USA

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