Heegaard gradient and virtual fibers

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.

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

References in corpus (2)

• Large embedded balls and Heegaard genus in negative curvature
• Period three actions on the three-sphere