New invariants in the theory of knots. (English) Zbl 0673.57007

On the geometry of differentiable manifolds, Workshop, Rome/Italy 1986, Astérisque 163-164, 137-219 (1988).
[For the entire collection see Zbl 0666.00013.]
The author makes excellent use of diagrams and pictures to help the reader understand proofs of many of the important theorems relating to the numerous polynomial invariants of links introduced in the last five years.
A listing of section titles gives some idea of the range of material covered. I. Introduction, II. The Bracket Polynomial, III. Alternating Knots and Links, IV. Braids and Diagrams, V. Generalized Polynomials, VI. Graphs and Statistical Physics, VII. The Bracket and the Tutte Polynomial, VIII. From Graph Theory to Knot Theory, IX. The Knot Theory of Imbedded Graphs.
A good deal of the paper is a continuation of work begun in the author’s: On knots (1987; Zbl 0627.57002).
Reviewer: L.P.Neuwirth


57M25 Knots and links in the \(3\)-sphere (MSC2010)
57M15 Relations of low-dimensional topology with graph theory