Title : On mutations and Vassiliev invariants (not) contained in knot polynomials
Speaker : Alexander Stoimenow (Kyungpook National University)
Abstract :

It is known that the Brandt-Lickorish-Millett-Ho polynomial $Q$ contains Casson's knot invariant. Whether there are (essentially) other Vassiliev knot invariants obtainable from $Q$ is an open problem. We show that this is not so up to degree $\le 9$. We also give the (apparently) first example of knots not distinguished by 2-cable HOMFLY polynomials, which are not mutants. Our calculations provide evidence against the conjecture that Vassiliev knot invariants of degree $\le 10$ are determined by the HOMFLY and Kauffman polynomial and their 2-cables, and for the existence of algebras of such Vassiliev invariants not isomorphic to the algebras of their weight systems.

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