Higher-Dimensional Algebra IV: 2-Tangles
Quantum Algebra
2007-05-23 v3 Algebraic Topology
Category Theory
Abstract
Just as knots and links can be algebraically described as certain morphisms in the category of tangles in 3 dimensions, compact surfaces smoothly embedded in R^4 can be described as certain 2-morphisms in the 2-category of `2-tangles in 4 dimensions'. Using the work of Carter, Rieger and Saito, we prove that this 2-category is the `free semistrict braided monoidal 2-category with duals on one unframed self-dual object'. By this universal property, any unframed self-dual object in a braided monoidal 2-category with duals determines an invariant of 2-tangles in 4 dimensions.
Cite
@article{arxiv.math/9811139,
title = {Higher-Dimensional Algebra IV: 2-Tangles},
author = {John C. Baez and Laurel Langford},
journal= {arXiv preprint arXiv:math/9811139},
year = {2007}
}
Comments
64 pages LaTeX with 35 encapsulated Postscript figures