Volume 11, issue 2 (2011)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 4, 1883–2507
Issue 3, 1259–1881
Issue 2, 635–1258
Issue 1, 1–633

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Unexpected local minima in the width complexes for knots

Alexander Zupan

Algebraic & Geometric Topology 11 (2011) 1097–1105
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.

Keywords
width complex, thin position, unknot
Mathematical Subject Classification 2010
Primary: 57M25, 57M27
References
Publication
Received: 20 September 2010
Revised: 15 January 2011
Accepted: 16 January 2011
Published: 1 April 2011
Authors
Alexander Zupan
Department of Mathematics
University of Iowa
14 MacLean Hall
Iowa City IA 52242
USA
http://math.uiowa.edu/~azupan