A few weight systems arising from intersection graphs

Details A few weight systems arising from intersection graphs A few weight systems arising from intersection graphs

2000-04-12

arxiv.org/abs/math/0004080v3

Michigan Math. J., vol. 51, no. 3, 2003, pp. 509-536

Mathematics

Geometric Topology

20 pages. This version has been substantially revised. The results are largely the same, but the proofs have been reconceptual

Scientific paper

We show that the adjacency matrices of the intersection graphs of chord diagrams satisfy the 2-term relations of Bar-Natan and Garoufalides [bg], and hence give rise to weight systems. Among these weight systems are those associated with the Conway and HOMFLYPT polynomials. We extend these ideas to looking at a space of {\it marked} chord diagrams modulo an extended set of 2-term relations, define a set of generators for this space, and again derive weight systems from the adjacency matrices of the (marked) intersection graphs. Among these weight systems are those associated with the Kauffman polynomial.

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