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arxiv: math/9811139 · v3 · pith:64IXFQI5new · submitted 1998-11-24 · 🧮 math.QA · math.AT· math.CT

Higher-Dimensional Algebra IV: 2-Tangles

John C. Baez , Laurel Langford This is my paper
classification 🧮 math.QA math.ATmath.CT
keywords categorytanglesdimensionsbraidedcertaindescribeddualsmonoidal
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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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