Heegaard gradient and virtual fibers

Details Heegaard gradient and virtual fibers Heegaard gradient and virtual fibers

2004-11-10

arxiv.org/abs/math/0411219v2

Geom. Topol. 9(2005) 2227-2259

Mathematics

Geometric Topology

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper51.abs.html

Scientific paper

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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