2-Tangles
q-alg
2008-02-03 v4 Quantum Algebra
Abstract
Just as links may be algebraically described as certain morphisms in the category of tangles, compact surfaces smoothly embedded in R^4 may be described as certain 2-morphisms in the 2-category of `2-tangles in 4 dimensions'. In this announcement we give a purely algebraic characterization of the 2-category of unframed unoriented 2-tangles in 4 dimensions as the `free semistrict braided monoidal 2-category with duals on one unframed self-dual object'. A forthcoming paper will contain a proof of this result using the movie moves of Carter, Rieger and Saito. We comment on how one might use this result to construct invariants of 2-tangles.
Cite
@article{arxiv.q-alg/9703033,
title = {2-Tangles},
author = {John C. Baez and Laurel Langford},
journal= {arXiv preprint arXiv:q-alg/9703033},
year = {2008}
}
Comments
12 pages LaTeX, 3 encapsulated Postscript figures, corrected definition of "unframed object"