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A locally minimal, but not globally minimal, bridge position of a knot

Published online by Cambridge University Press:  25 April 2013

MAKOTO OZAWA  and
KAZUTO TAKAO
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
KAZUTO TAKAO
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, 1-1 Machikaneyama-cho, Toyonaka, Osaka, 560-0043, Japan. e-mail: kazutotakao@gmail.com
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Abstract

We give a locally minimal, but not globally minimal, bridge position of a knot, that is, an unstabilized, nonminimal bridge position of a knot. It implies that a bridge position cannot always be simplified so that the bridge number monotonically decreases to the minimal.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 155 , Issue 1 , July 2013 , pp. 181 - 190
Copyright
Copyright © Cambridge Philosophical Society 2013 

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