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Heegaard gradient and virtual fibers

Maher, Joseph (2005) Heegaard gradient and virtual fibers. Geometry and Topology, 9 (51). pp. 2227-2259. ISSN 1465-3060. doi:10.2140/gt.2005.9.2227.

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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.

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Additional Information:© 2005 Geometry & Topology Publications. Submitted to GT on 14 January 2005. Paper accepted 26 November 2005. Paper published 3 December 2005. Proposed: Cameron Gordon; Seconded: David Gabai, Joan Birman. I would like to thank Ian Agol for informing me of Corollary 1.3, and Nathan Dunfield for pointing out various mistakes in preliminary versions of this paper. I would also like to thank Marc Lackenby, Hyam Rubinstein, Jason Manning and Martin Scharlemann for helpful conversations.
Subject Keywords:Heegaard splitting, virtual fiber, hyperbolic 3-manifold
Issue or Number:51
Classification Code:AMS subject classification. Primary: 57M10. Secondary: 57M50.
Record Number:CaltechAUTHORS:MAHgt05
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1175
Deposited By: Archive Administrator
Deposited On:02 Jan 2006
Last Modified:08 Nov 2021 19:08

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