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2011 Flipping bridge surfaces and bounds on the stable bridge number
Jesse Johnson, Maggy Tomova
Algebr. Geom. Topol. 11(4): 1987-2005 (2011). DOI: 10.2140/agt.2011.11.1987

Abstract

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 2n1 bridges respectively for which any common perturbation has at least 3n4 bridges. We generalize both of these results to bridge surfaces for knots in any 3–manifold.

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Jesse Johnson. Maggy Tomova. "Flipping bridge surfaces and bounds on the stable bridge number." Algebr. Geom. Topol. 11 (4) 1987 - 2005, 2011. https://doi.org/10.2140/agt.2011.11.1987

Information

Received: 17 April 2010; Revised: 29 March 2011; Accepted: 15 May 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1231.57007
MathSciNet: MR2826930
Digital Object Identifier: 10.2140/agt.2011.11.1987

Subjects:
Primary: 57M25, 57M27, 57M50

Rights: Copyright © 2011 Mathematical Sciences Publishers

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Vol.11 • No. 4 • 2011
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