低次元トポロジーセミナー


2018/11/20(Tue)

10:30--12:00 理学部 b棟 b342/346

小鳥居 祐香

理化学研究所, 大阪大学

On combinatorial formulas of finite type invariant for knots

This research is a joint work with Noboru Ito (Univ. of Tokyo). In 1990, Vassiliev introduced powerful filtered knot invariants called finite type invariants. In order to present a Vassiliev invariant by a combinatorial formula, Polyak and Viro introduced Gauss diagram formulas. Goussarov showed that any integer-valued finite type invariant of knots can be presented as a Gauss diagram formula. However, we do not have an algorithm to obtain a Gauss diagram formula for a given finite type invariant of knots. In this talk, we give some Gauss diagram formulas for the finite type invariant of degree three.