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Unexpected local minima in the width complexes for knots
by
Alexander Zupan
The University of Iowa
In 1934, Goeritz exhibited a nontrivial diagram of the unknot that such any sequence of Reidemeister moves converting this diagram to the zero crossing diagram increases the number of crossings of the diagram. As an analogue, we produce a nontrivial embedding of the unknot such that any isotopy from this embedding to the thin position of the unknot increases knot width in the sense of Gabai. This resolves a question of Scharlemann, and we apply our result to demonstrate that the width complexes for knots developed by Schultens have infinitely many local minima that are not global minima.
Paper reference: arXiv:1008.5003
Date received: October 20, 2010
Copyright © 2010 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbbr-04.