The Jones polynomial of an unknotting number one knot
The author presents a necessary condition for a knot in \(S^3\) to have unknotting number one, involving the Jones polynomial, the Conway polynomial and the signature. The condition is derived from surgery formulas for the Casson invariant of the 2-fold branched cover of \(S^3\) branched over the knot [cf. \textit{S. Boyer} and \textit{D. Lines}, J. Reine Angew. Math. 405, 181-220 (1990; Zbl 0691.57004); \textit{D. Mullins}, Topology 32, No. 2, 419-438 (1993; Zbl 0784.57003); the author, Osaka J. Math. 32, No. 1, 193-206 (1995; Zbl 0861.57014)].
scientific article; zbMATH DE number 1308036
scientific article