Subject: categories: HDA4: 2-Tangles

From: john baez <[email-masked]>
Date: Mon, 23 Nov 1998 20:08:31 -0800 (PST)

The following preprint is now available at the places listed below.
Comments and corrections are welcome!

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Higher-Dimensional Algebra IV: 2-Tangles
John C. Baez, Laurel Langford

Just as knots and links can be algebraically described as certain
morphisms in the category of tangles in 3 dimensions, compact surfaces
smoothly embedded in R^4 can be described as certain 2-morphisms in
the 2-category of `2-tangles in 4 dimensions'.   Using the work of
Carter, Rieger and Saito, we prove that this 2-category is the `free
semistrict braided monoidal 2-category with duals on one unframed
self-dual object'.  By this universal property, any unframed self-dual
object in a braided monoidal 2-category with duals determines an
invariant of 2-tangles in 4 dimensions.

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This paper is math.QA/981139 on the mathematics preprint server,
so you can get it at:

http://xxx.lanl.gov/abs/math.QA/9811139

It's also available as a Postscript file at my website:

http://math.ucr.edu/home/baez/hda4.ps

If you have any trouble, let me know and I can send you a copy.