- Cite this article as:
- Baez, J.C. & Langford, L. Letters in Mathematical Physics (1998) 43: 187. doi:10.1023/A:1007449529401
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.