Higher-Dimensional Algebra IV: 2-Tangles

Details Higher-Dimensional Algebra IV: 2-Tangles Higher-Dimensional Algebra IV: 2-Tangles

1998-11-24

arxiv.org/abs/math/9811139v3

Adv. Math. 180 (2003), 705-764.

Mathematics

Quantum Algebra

64 pages LaTeX with 35 encapsulated Postscript figures

Scientific paper

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.

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