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2007 Multiple bridge surfaces restrict knot distance
Maggy Tomova
Algebr. Geom. Topol. 7(2): 957-1006 (2007). DOI: 10.2140/agt.2007.7.957

Abstract

Suppose M is a closed irreducible orientable 3–manifold, K is a knot in M, P and Q are bridge surfaces for K and K is not removable with respect to Q. We show that either Q is equivalent to P or d(K,P)2χ(QK). If K is not a 2–bridge knot, then the result holds even if K is removable with respect to Q. As a corollary we show that if a knot in S3 has high distance with respect to some bridge sphere and low bridge number, then the knot has a unique minimal bridge position.

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Maggy Tomova. "Multiple bridge surfaces restrict knot distance." Algebr. Geom. Topol. 7 (2) 957 - 1006, 2007. https://doi.org/10.2140/agt.2007.7.957

Information

Received: 5 April 2007; Accepted: 7 May 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1142.57005
MathSciNet: MR2336246
Digital Object Identifier: 10.2140/agt.2007.7.957

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

Rights: Copyright © 2007 Mathematical Sciences Publishers

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