Title : On the Jones polynomials of $6_1$-like ribbon knots
Speaker : Tsuyoshi Sakai (Nihon University)
Abstract :

In this talk we give a relation between the first derivative at $-1$ and the third derivative at 1 of the Jones polynomial of $6_1$-like ribbon knot, which is a special class of ribbon knots. \smallskip \noindent {\sc Theorem.} {\it Let $K$ be a $6_1$-like ribbon knot. Let $J_K(t)$ be the Jones polynomial of $K$. Then the following holds.} $$2J_K^{\prime \prime \prime}(1) =- 9J_K^{\prime}(-1) - 72.$$ In this talk we give some results obtained from formulas for the first derivative at $-1$ and the third derivative at 1 of the Jones polynomial of ribbon knots of 1-fusion.

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