Geodesic
The Reidemeister graph is a complete knot invariant
Barbensi, Agnese1 ; Celoria, Daniele1
1Mathematical Institute, University of Oxford, Oxford, United Kingdom
Algebraic and Geometric Topology, Tome 20 (2020) no. 2, pp. 643-698
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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.

DOI : 10.2140/agt.2020.20.643
Classification : 57M25
Keywords: knots, knot diagrams, graph, complete knot invariant

Barbensi, Agnese  1   ; Celoria, Daniele  1

1 Mathematical Institute, University of Oxford, Oxford, United Kingdom 
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Barbensi, Agnese; Celoria, Daniele. The Reidemeister graph is a complete knot invariant. Algebraic and Geometric Topology, Tome 20 (2020) no. 2, pp. 643-698. doi: 10.2140/agt.2020.20.643

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