Abstract

J. Hempel’s definition of the distance of a Heegaard surface generalizes to a notion of complexity for any knot that 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 suficiently high powers of pseudo-Anosov maps have minimal bridge presentations which are thin.

Keywords

Heegaard splitting, curve complex

Mathematical Subject Classification

Primary: 57M25, 57M27

Authors