Higher-Dimensional Algebra IV: 2-Tangles

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
64 pages LaTeX with 35 encapsulated Postscript figures

Keywords

Quantum Algebra, Algebraic Topology, Category Theory

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/96718

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9811139
 http://arxiv.org/abs/math/9811139
 Adv. Math. 180 (2003), 705-764.

Collections

arXiv