A bracket polynomial for graphs

Details A bracket polynomial for graphs A bracket polynomial for graphs

2008-08-25

arxiv.org/abs/0808.3392v2

Mathematics

Geometric Topology

26 pages, 10 figures Slight further revisions will be made before publication in the Journal of Knot Theory and its Ramificati

Scientific paper

A knot diagram has an associated looped interlacement graph, obtained from the intersection graph of the Gauss diagram by attaching loops to the vertices that correspond to negative crossings. This construction suggests an extension of the Kauffman bracket to an invariant of looped graphs, and an extension of Reidemeister equivalence to an equivalence relation on looped graphs. The graph bracket polynomial can be defined recursively using the same pivot and local complementation operations used to define the interlace polynomial, and it gives rise to a graph Jones polynomial that is invariant under the graph Reidemeister moves.

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