A polynomial invariant of knots and links
This paper describes the construction of an invariant of oriented links which is a homogeneous Laurent polynomial of total degree 0 in 3 variables, and which specializes to the Conway and Jones polynomials. Such invariants were discovered independently and almost simultaneously by a number of workers [cf. the joint announcement by \textit{P. Freyd} et al., Bull. Am. Math. Soc., New Ser. 12, 239-246 (1985; Zbl 0572.57002)]. Given a projection of the link and a specified resolution to an unlink, a Laurent polynomial may be defined via generalizing Conway identities. It is first shown to be independent of the resolution, and then to be invariant under Reidemeister moves. Thus it is indeed an invariant of the oriented isotopy type of the link. It is also shown that there are distinct prime knots having the same polynomial, and links with homeomorphic complements which have different polynomials.
scientific article; zbMATH DE number 3994561