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19 January 2021
 
  » arxiv » math.QA/9811139

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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
AbstractJust 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
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