Topological and physical link theory are distinct

Alexander Coward and Joel Hass

Vol. 276 (2015), No. 2, 387–400

DOI: 10.2140/pjm.2015.276.387

Abstract

Physical knots and links are one-dimensional submanifolds of ${ℝ}^{\mathfrak{3}}$ 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