The Intersection Graph Conjecture for Loop Diagrams

Details The Intersection Graph Conjecture for Loop Diagrams The Intersection Graph Conjecture for Loop Diagrams

1998-07-08

arxiv.org/abs/math/9807033v4

Journal of Knot Theory and Its Ramifications, Vol. 9, No. 2 (2000) 187-211

Mathematics

Geometric Topology

23 pages, many figures. arXiv admin note: Figures 1, 2, 5 and 11 included in sources but in format not supported by arXiv

Scientific paper

Vassiliev invariants can be studied by studying the spaces of chord diagrams associated with singular knots. To these chord diagrams are associated the intersection graphs of the chords. We extend results of Chmutov, Duzhin and Lando to show that these graphs determine the chord diagram if the graph has at most one loop. We also compute the size of the subalgebra generated by these "loop diagrams."

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