## Higher-dimensional algebra IV: 2-Tangles

by
John C. Baez
,
Laurel Langford

Citations: | 35 - 10 self |

### BibTeX

@MISC{Baez_higher-dimensionalalgebra,

author = {John C. Baez and Laurel Langford},

title = {Higher-dimensional algebra IV: 2-Tangles},

year = {}

}

### Years of Citing Articles

### OpenURL

### 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. 1