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2011 Unexpected local minima in the width complexes for knots
Alexander Zupan
Algebr. Geom. Topol. 11(2): 1097-1105 (2011). DOI: 10.2140/agt.2011.11.1097

Abstract

In [Pacific J. Math. 239 (2009) 135–156], Schultens defines the width complex for a knot in order to understand the different positions a knot can occupy in S3 and the isotopies between these positions. She poses several questions about these width complexes; in particular, she asks whether the width complex for a knot can have local minima that are not global minima. In this paper, we find an embedding of the unknot 01 that is a local minimum but not a global minimum in the width complex for 01, resolving a question of Scharlemann. We use this embedding to exhibit for any knot K infinitely many distinct local minima that are not global minima of the width complex for K.

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Alexander Zupan. "Unexpected local minima in the width complexes for knots." Algebr. Geom. Topol. 11 (2) 1097 - 1105, 2011. https://doi.org/10.2140/agt.2011.11.1097

Information

Received: 20 September 2010; Revised: 15 January 2011; Accepted: 16 January 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1227.57015
MathSciNet: MR2792375
Digital Object Identifier: 10.2140/agt.2011.11.1097

Subjects:
Primary: 57M25, 57M27

Rights: Copyright © 2011 Mathematical Sciences Publishers

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Vol.11 • No. 2 • 2011
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