Distance and bridge position

Details Distance and bridge position Distance and bridge position

2003-08-29

arxiv.org/abs/math/0308297v1

Mathematics

Geometric Topology

14 pages, 4 figures

Scientific paper

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.

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