Title : The $2$-loop polynomial for knots of genus $1$
Speaker : Tomotada Ohtsuki (RIMS, Kyoto University)
Abstract :

The 2-loop polynomial is a polynomial presenting the 2-loop part of the Kontsevich invariant of knots. The values of the 2-loop polynomial has been calculated so far only for some particular classes of knots, such as torus knots and knots with the trivial Alexander polynomial. In this talk, I explain that the 2-loop polynomial of a knot can be presented by finite type invariants of a trivalent graph which is a spine of a Seifert surface of the knot. In particular, I give an explicit formula of the 2-loop polynomial for the knots of genus 1.

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