Displaying similar documents to “Combinatorics and topology - François Jaeger's work in knot theory”

Invariants of piecewise-linear knots

Richard Randell (1998)

Banach Center Publications

Similarity:

We study numerical and polynomial invariants of piecewise-linear knots, with the goal of better understanding the space of all knots and links. For knots with small numbers of edges we are able to find limits on polynomial or Vassiliev invariants sufficient to determine an exact list of realizable knots. We thus obtain the minimal edge number for all knots with six or fewer crossings. For example, the only knot requiring exactly seven edges is the figure-8 knot.

Adequacy of Link Families

Slavik Jablan, Ljiljana Radović, Radmila Sazdanović (2010)

Publications de l'Institut Mathématique

Similarity:

Search for different links with the same Jones' type polynomials: Ideas from graph theory and statistical mechanics

Józef Przytycki (1995)

Banach Center Publications

Similarity:

We describe in this talk three methods of constructing different links with the same Jones type invariant. All three can be thought as generalizations of mutation. The first combines the satellite construction with mutation. The second uses the notion of rotant, taken from the graph theory, the third, invented by Jones, transplants into knot theory the idea of the Yang-Baxter equation with the spectral parameter (idea employed by Baxter in the theory of solvable models in statistical...