#### Volume 9, issue 4 (2005)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060
Heegaard gradient and virtual fibers

### Joseph Maher

Geometry & Topology 9 (2005) 2227–2259
 arXiv: math.GT/0411219
##### 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
Primary: 57M10
Secondary: 57M50
##### Publication
Received: 14 January 2005
Accepted: 26 November 2005
Published: 3 December 2005
Proposed: Cameron Gordon
Seconded: David Gabai, Joan Birman
##### Authors
 Joseph Maher Mathematics 253-37 California Institute of Technology Pasadena California 91125 USA