Bridge number, Heegaard genus and non-integral Dehn surgery
Geometric Topology
2013-11-20 v2
Abstract
We show there exists a linear function w: N->N with the following property. Let K be a hyperbolic knot in a hyperbolic 3-manifold M admitting a non-longitudinal S^3 surgery. If K is put into thin position with respect to a strongly irreducible, genus g Heegaard splitting of M then K intersects a thick level at most 2w(g) times. Typically, this shows that the bridge number of K with respect to this Heegaard splitting is at most w(g), and the tunnel number of K is at most w(g) + g-1.
Keywords
Cite
@article{arxiv.1202.0263,
title = {Bridge number, Heegaard genus and non-integral Dehn surgery},
author = {Kenneth L. Baker and Cameron Gordon and John Luecke},
journal= {arXiv preprint arXiv:1202.0263},
year = {2013}
}
Comments
76 page, 48 figures; referee comments incorporated and typos fixed; accepted at TAMS