Intersecting Braids and Intersecting Knot Theory
High Energy Physics - Theory
2009-09-01 v1 Quantum Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.hep-th/9309136,
title = {Intersecting Braids and Intersecting Knot Theory},
author = {Daniel Armand-Ugon and Rodolfo Gambini and Pablo Mora},
journal= {arXiv preprint arXiv:hep-th/9309136},
year = {2009}
}
Comments
14 pages (6 figures included)