Topological and physical link theory are distinct. (English) Zbl 1326.53008

Coward, Alexander; Hass, Joel

Pac. J. Math. 276, No. 2, 387-400 (2015).

The present paper is dedicated to the study of knots theory from two points of view: physical and topological. The authors present physical knots and links like one-dimensional submanifolds of \(\mathbb{R}^{3}\) with fixed length and thickness. Also, in their proofs the authors use the isotopy classes. The authors also develop a particular case, namely a “Gordian split link”: a two-component link that is split in the classical theory but cannot be split with a physical isotopy. The paper consists of 5 parts; in the last parts some interesting open problems are also given.

Reviewer: Laurian Ioan Piscoran (Baia Mare)

MSC:

53A04	Curves in Euclidean and related spaces
57M25	Knots and links in the \(3\)-sphere (MSC2010)

Keywords:

physical knot theory; Gordian, split link