Title : Knots with given finite type invariants and Conway polynomial
(a joint work with Yasutaka Nakanishi)
Speaker : Yoshiyuki Ohyama (Tokyo Woman's Christian University)
Abstract :

In this talk, we show that for any given pair of a natural number $n$ and a knot $K$, there exist infinitely many knots $J_{m}$ $(m=1,2,\ldots)$ which satisfy the following: (1) for any $v_{k}$ $(k=1,2, \ldots , n)$, $v_{k}(J_{m})=v_{k}(K)$ and (2) $\nabla_{J_m}(z)=\nabla_{K}(z)$, where $v_{k}$ is a Vassiliev invariant of order $k$ and $\nabla_{K}(z)$ is the Conway polynomial of $K$.

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