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Higher-Dimensional Algebra IV: 2-Tangles | | John C. Baez
; Laurel Langford
; | | Date: |
24 Nov 1998 | | Subject: | Quantum Algebra; Category Theory; Algebraic Topology | math.QA math.AT math.CT | | 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. | | Source: | arXiv, math.QA/9811139 | | Services: | Forum | Review | PDF | Favorites | |
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