Vol. 276, No. 2, 2015

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ISSN: 0030-8730
Topological and physical link theory are distinct

Alexander Coward and Joel Hass

Vol. 276 (2015), No. 2, 387–400
Abstract

Physical knots and links are one-dimensional submanifolds of 3 with fixed length and thickness. We show that isotopy classes in this category can differ from those of classical knot and link theory. In particular we exhibit a Gordian split link, a two-component link that is split in the classical theory but cannot be split with a physical isotopy.

Keywords
physical knot theory, Gordian, split link
Mathematical Subject Classification 2010
Primary: 53A04, 57M25
Milestones
Received: 6 August 2012
Revised: 10 September 2013
Accepted: 16 September 2013
Published: 15 July 2015
Authors
Alexander Coward
Department of Mathematics
UC Berkeley
970 Evans Hall #3840
Berkeley, CA 94720
United States
Joel Hass
Mathematics Department
University of California
Davis, CA 95616
United States