ar X iv : q - a lg / 9 70 30 33 v 1 1 8 M ar 1 99 7 2 - Tangles
نویسنده
چکیده
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 4 dimensions’. In this announcement we give a purely algebraic characterization of the 2-category of unframed unoriented 2-tangles in 4 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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