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2007 Mutant knots and intersection graphs
Sergei Chmutov, Sergei Lando
Algebr. Geom. Topol. 7(3): 1579-1598 (2007). DOI: 10.2140/agt.2007.7.1579

Abstract

We prove that if a finite order knot invariant does not distinguish mutant knots, then the corresponding weight system depends on the intersection graph of a chord diagram rather than on the diagram itself. Conversely, if we have a weight system depending only on the intersection graphs of chord diagrams, then the composition of such a weight system with the Kontsevich invariant determines a knot invariant that does not distinguish mutant knots. Thus, an equivalence between finite order invariants not distinguishing mutants and weight systems depending only on intersections graphs is established. We discuss the relationship between our results and certain Lie algebra weight systems.

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Sergei Chmutov. Sergei Lando. "Mutant knots and intersection graphs." Algebr. Geom. Topol. 7 (3) 1579 - 1598, 2007. https://doi.org/10.2140/agt.2007.7.1579

Information

Received: 16 May 2007; Revised: 14 September 2007; Accepted: 17 September 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1158.57013
MathSciNet: MR2366172
Digital Object Identifier: 10.2140/agt.2007.7.1579

Subjects:
Primary: 57M15, 57M25
Secondary: 05C10, 57M27

Rights: Copyright © 2007 Mathematical Sciences Publishers

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Vol.7 • No. 3 • 2007
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