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Search for different links with the same Jones' type polynomials: Ideas from graph theory and statistical mechanics

Józef Przytycki (1995)

Banach Center Publications

We describe in this talk three methods of constructing different links with the same Jones type invariant. All three can be thought as generalizations of mutation. The first combines the satellite construction with mutation. The second uses the notion of rotant, taken from the graph theory, the third, invented by Jones, transplants into knot theory the idea of the Yang-Baxter equation with the spectral parameter (idea employed by Baxter in the theory of solvable models in statistical mechanics)....

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