Thistlethwaite's theorem for virtual links

By Sergei Chmutov, J. Voltz. 2007

47 citations recorded by the source corpus.

The celebrated Thistlethwaite theorem relates the Jones polynomial of a link with the Tutte polynomial of the corresponding planar graph. We give a generalization of this theorem to virtual links. In this case, the graph will be embedded into a (higher genus) surface. For such graphs we use the generalization of the Tutte polynomial discovered by B.Bollobas and O.Riordan.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0c18ee404ed2e640616f26e2d77ced705670016a

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In Discrete Mathematics and Combinatorics

1. Joanna A. Ellis-Monaghan
2. Iain Moffatt
3. Martin Loebl

In Geometry and Topology

1. Joanna A. Ellis-Monaghan
2. Iain Moffatt
3. Martin Loebl

In Mathematical Physics

1. Joanna A. Ellis-Monaghan
2. Iain Moffatt
3. Martin Loebl

Citations in the corpus

• Twisted duality for embedded graphs (2009, methodology): “A third extension of Thistlethwaite’s result was given by Chmutov and Voltz in [22], where the Jones polynomial of an arbitrary virtual link was shown to be an evaluation of the topochromatic polynomial.”
• The chromatic polynomial of fatgraphs and its categorification (2005, background): “enus zero, Chmutov and Pak’s result specialises to Thistlethwaite’s Theorem. We note there is currently interest in connections between knots and their polynomials and fatgraphs and their polynomials [10, 13, 21, 29, 30]. This discussion of motivates the categorications of fatgraph polynomials propo”