Intersecting Braids and Intersecting Knot Theory

Details Intersecting Braids and Intersecting Knot Theory Intersecting Braids and Intersecting Knot Theory

1993-09-24

arxiv.org/abs/hep-th/9309136v1

J.Knot Theor.Ramifications 4:1-12,1995

Physics

High Energy Physics

High Energy Physics - Theory

14 pages (6 figures included)

Scientific paper

An extension of the Artin Braid Group with new operators that generate double and triple intersections is considered. The extended Alexander theorem, relating intersecting closed braids and intersecting knots is proved for double and triple intersections, and a counter example is given for the case of quadruple intersections. Intersecting knot invariants are constructed via Markov traces defined on intersecting braid algebra representations, and the extended Turaev representation is discussed as an example. Possible applications of the formalism to quantum gravity are discussed.

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