Topological and physical knot theory are distinct
arXiv:1203.4019 · doi:10.2140/pjm.2015.276.387
Abstract
Physical knots and links are one-dimensional submanifolds of R^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.
8 page, 6 figures