Abstract
Just as links may be algebraically described as certain morphisms in the category of tangles, compact surfaces smoothly embedded in R4 may be described as certain 2-morphisms in the 2-category of ‘2-tangles in four dimensions’. In this announcement we give a purely algebraic characterization of the 2-category of unframed unoriented 2-tangles in four dimensions as the ‘free semistrict braided monoidal 2-category with duals on one unframed self-dual object’. A forthcoming paper will contain a proof of this result using the movie moves of Carter, Rieger and Saito. We comment on how one might use this result to construct invariants of 2-tangles.
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Baez, J.C., Langford, L. 2-Tangles. Letters in Mathematical Physics 43, 187–197 (1998). https://doi.org/10.1023/A:1007449529401
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DOI: https://doi.org/10.1023/A:1007449529401