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The Reidemeister graph is a complete knot invariant

Agnese Barbensi and Daniele Celoria

Algebraic & Geometric Topology 20 (2020) 643–698
Abstract

We describe two locally finite graphs naturally associated to each knot type K, called Reidemeister graphs. We determine several local and global properties of these graphs and prove that in one case the graph-isomorphism type is a complete knot invariant up to mirroring. Lastly, we introduce another object, relating the Reidemeister and Gordian graphs, and determine some of its properties.

Keywords
knots, knot diagrams, graph, complete knot invariant
Mathematical Subject Classification 2010
Primary: 57M25
References
Publication
Received: 24 January 2018
Revised: 7 January 2019
Accepted: 1 April 2019
Published: 23 April 2020
Authors
Agnese Barbensi
Mathematical Institute
University of Oxford
Oxford
United Kingdom
Daniele Celoria
Mathematical Institute
University of Oxford
Oxford
United Kingdom