Virtual Betti numbers of genus 2 bundles

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.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper19.abs.htm