Date: Tue, 18 Mar 1997 10:28:37 -0400 (AST)
Subject: 2-Tangles 
 
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