From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/341 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: 2-Tangles Date: Tue, 18 Mar 1997 10:28:09 -0400 (AST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241016902 25275 80.91.229.2 (29 Apr 2009 14:55:02 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:55:02 +0000 (UTC) To: categories Original-X-From: cat-dist Tue Mar 18 10:29:38 1997 Original-Received: by mailserv.mta.ca; id AA23682; Tue, 18 Mar 1997 10:28:09 -0400 Original-Lines: 33 Xref: news.gmane.org gmane.science.mathematics.categories:341 Archived-At: Date: Tue, 18 Mar 1997 00:09:18 -0500 (EST) From: John Baez Here is a short paper summarizing some work done by my student Laurel Langford. ----------------------------------------------------------------------- 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