The Reidemeister graph is a complete knot invariant

Barbensi, Agnese; Celoria, Daniele

doi:10.2140/agt.2020.20.643

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The Reidemeister graph is a complete knot invariant

Agnese Barbensi and Daniele Celoria

Algebraic & Geometric Topology 20 (2020) 643–698

DOI: 10.2140/agt.2020.20.643

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

Volume 20, issue 2 (2020)