Flipping bridge surfaces and bounds on the stable bridge number

Original · EN

We show that if K is a knot in S³ and Σ is a bridge sphere for K with high distance and 2n punctures, the number of perturbations of K required to interchange the two balls bounded by Σ via an isotopy is n. We also construct a knot with two different bridge spheres with 2n and 2n-1 bridges respectively for which any common perturbation has at least 3n-1 bridges. We generalize both of these results to bridge surfaces for knots in any 3-manifold.