2-Tangles

2-Tangles

[categories]

Date: Tue, 18 Mar 1997 00:09:18 -0500 (EST)
From: John Baez <baez@phys.psu.edu>

Here is a short paper summarizing some work done by my student
Laurel Langford.

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2-Tangles
John C. Baez and Laurel Langford

Just as links may be algebraically described as certain morphisms in
the category of tangles, compact surfaces smoothly embedded in R^4
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.

One can get a Postscript version of this paper at

http://math.ucr.edu/home/baez/2tang.ps

or by anonymous ftp to math.ucr.edu, where it's in the
directory pub/baez, as the file

2tang.ps