Flipping bridge surfaces and bounds on the stable bridge number

Jesse Johnson; Maggy Tomova

doi:10.2140/agt.2011.11.1987

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arXiv · 0908.3690

Flipping bridge surfaces and bounds on the stable bridge number

Jesse Johnson·Maggy Tomova

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Abstract

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

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BibTeX RIS

Jesse Johnson, Maggy Tomova. 2010-04-18. Flipping bridge surfaces and bounds on the stable bridge number. https://doi.org/10.2140/agt.2011.11.1987

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