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

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### 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