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The Reidemeister graph
is a complete knot invariant
Agnese Barbensi and Daniele Celoria |
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Algebraic & Geometric Topology 20 (2020) 643–698
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Abstract |
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We describe two locally finite graphs naturally associated to each knot type , 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. |
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Keywords
knots, knot diagrams, graph, complete knot invariant
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Mathematical Subject Classification 2010
Primary: 57M25
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References |
Publication
Received: 24 January 2018
Revised: 7 January 2019
Accepted: 1 April 2019
Published: 23 April 2020
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Authors |
| Agnese Barbensi | |
| Mathematical Institute University of Oxford Oxford United Kingdom |
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| Daniele Celoria | |
| Mathematical Institute University of Oxford Oxford United Kingdom |
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