Geometry & Topology 9 (2005) 2227–2259

DOI: 10.2140/gt.2005.9.2227

Abstract

We show that if a closed hyperbolic 3–manifold has infinitely many finite covers of bounded Heegaard genus, then it is virtually fibered. This generalizes a theorem of Lackenby, removing restrictions needed about the regularity of the covers. Furthermore, we can replace the assumption that the covers have bounded Heegaard genus with the weaker hypotheses that the Heegaard splittings for the covers have Heegaard gradient zero, and also bounded width, in the sense of Scharlemann–Thompson thin position for Heegaard splittings.

Keywords

Heegaard splitting, virtual fiber, hyperbolic 3–manifold

Mathematical Subject Classification

Primary: 57M10

Secondary: 57M50

References

Publication

Received: 14 January 2005
Accepted: 26 November 2005
Published: 3 December 2005
Proposed: Cameron Gordon
Seconded: David Gabai, Joan Birman

Authors