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Nonminimal bridge positions of torus knots are stabilized

Published online by Cambridge University Press:  04 May 2011

MAKOTO OZAWA
MAKOTO OZAWA*
Affiliation:
Department of Natural Sciences, Faculty of Arts and Sciences, Komazawa University, 1-23-1 Komazawa, Setagaya-ku, Tokyo, 154-8525, Japan. e-mail: w3c@komazawa-u.ac.jp
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Abstract

We show that any nonminimal bridge decomposition of a torus knot is stabilized and that n-bridge decompositions of a torus knot are unique for any integer n. This implies that a knot in a bridge position is a torus knot if and only if there exists a torus containing the knot such that it intersects the bridge sphere in two essential loops.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 151 , Issue 2 , September 2011 , pp. 307 - 317
Copyright
Copyright © Cambridge Philosophical Society 2011

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