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