Heegaard gradient and virtual fibers

Maher, Joseph

doi:10.2140/gt.2005.9.2227

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Heegaard gradient and virtual fibers

Joseph Maher

Geometry & Topology 9 (2005) 2227–2259

DOI: 10.2140/gt.2005.9.2227

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

Mathematical Subject Classification 2000

Primary: 57M10

Secondary: 57M50

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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

Volume 9, issue 4 (2005)