Flipping bridge surfaces and bounds on the stable bridge number

Details Flipping bridge surfaces and bounds on the stable bridge number Flipping bridge surfaces and bounds on the stable bridge number

2009-08-25

arxiv.org/abs/0908.3690v2

Mathematics

Geometric Topology

20 pages, 7 figures

Scientific paper

We show that if $K$ is a knot in $S^3$ and $\Sigma$ 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 $\Sigma$ 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.

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