New points of view in knot theory. (English) Zbl 0785.57001
The author presents the modern point of view of knot theory along with its history, explaining the various polynomials which have been defined, along with the Vassiliev invariants. Her explanations are graceful, relaxed and not difficult to follow, as there are many examples and pictures illustrating the ideas. Many of the theorems cited are proved.
Reviewer: L.P.Neuwirth (Princeton)
MSC:
| 57M25 | Knots and links in the \(3\)-sphere (MSC2010) |
| 57N99 | Topological manifolds |
Keywords:
knot polynomial; knot group; \(R\)-matrices; quantum group; knot theory; Vassiliev invariantsOnline Encyclopedia of Integer Sequences:
Dimension of space of weight systems of chord diagrams.Dimension of primitive Vassiliev knot invariants of order n.
Conjectured numbers of Vassiliev invariants of knots.
Partial sums of A001935; at one time this was conjectured to agree with A007478.
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