A new polynomial invariant of knots and links. (English) Zbl 0572.57002

Freyd, P.; Yetter, D.; Hoste, J.; Lickorish, W. B. R.; Millett, K.; Ocneanu, A.

Bull. Am. Math. Soc., New Ser. 12, 239-246 (1985).

This note introduces a polynomial which extends both the Alexander-Conway and Jones invariants of links. The new invariant was discovered independently and almost simultaneously by four groups; an outline of each approach is given after a statement of the common result. (Yet another approach has been found by J. Przytycki and P. Traczyk, Univ. Warsaw, 1985.) The main theorem asserts that there is a unique homogeneous 3-variable Laurent polynomial invariant of isotopy classes of tame oriented links which satisfies a Conway identity and which takes the values 1 on the unknot.

Reviewer: J.Hillman

MSC:

57M25

Knots and links in the \(3\)-sphere (MSC2010)

Keywords:

Alexander-Conway polynomial; Jones polynomial; Laurent polynomial; tame oriented links

References:

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