Knot-theoretic ternary groups
Volume 247 / 2019
Fundamenta Mathematicae 247 (2019), 299-320
MSC: Primary 20N15, 57M25; Secondary 57M27, 03C05, 08A05.
DOI: 10.4064/fm611-11-2018
Published online: 13 June 2019
Abstract
We describe various properties and give several characterizations of ternary groups satisfying two axioms derived from the third Reidemeister move in knot theory. Using special attributes of such ternary groups, such as semi-commutativity, we construct a ternary invariant of curves immersed in compact surfaces, considered up to flat Reidemeister moves.
