Resumen de Distance and bridge position
J. Hempel's denition 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 suciently high powers of pseudo-Anosov maps have minimal bridge presentations which are thin.
