Mutant knots and intersection graphs

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. The converse statement is easy and well known. We discuss relationship between our results and certain Lie algebra weight systems.

13 pages, many figures

References in corpus (3)

• The universal Vassiliev-Kontsevich invariant for framed oriented links
• The universal Vassiliev invariant for the Lie superalgebra gl(1|1)
• Complete Invariant Graphs of Alternating Knots

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• Partial-dual genus polynomials and signed intersection graphs
• Tentative Structural Features of a Gapped RVB State in the Anisotropic Triangular Lattice
• The transition matroid of a 4-regular graph: an introduction
• Partial-dual genus polynomial as a weight system
• The sl(2)-weight system at c = 3/8 for graphs
• c-a-ca Mean Field RVB Model of CuNCN Physics. Structure Manifestations of the RVB Transitions