Distance and bridge position
Geometric Topology
2007-05-23 v1
Abstract
J. Hempel's definition of the distance of a Heegaard surface generalizes to a complexity for a knot which is in bridge position with respect to a Heegaard surface. Our main result is that the distance of a knot in bridge position is bounded above by twice the genus, plus the number of boundary components, of an essential surface in the knot complement. As a consequence knots constructed via sufficiently high powers of pseudo-Anosov maps have minimal bridge presentations which are thin.
Keywords
Cite
@article{arxiv.math/0308297,
title = {Distance and bridge position},
author = {David Bachman and Saul Schleimer},
journal= {arXiv preprint arXiv:math/0308297},
year = {2007}
}
Comments
14 pages, 4 figures