Letters in Mathematical Physics

, Volume 43, Issue 2, pp 187–197


  • John C. Baez
  • Laurel Langford

DOI: 10.1023/A:1007449529401

Cite this article as:
Baez, J.C. & Langford, L. Letters in Mathematical Physics (1998) 43: 187. doi:10.1023/A:1007449529401


Just as links may be algebraically described as certain morphisms in the category of tangles, compact surfaces smoothly embedded in R4 may be described as certain 2-morphisms in the 2-category of ‘2-tangles in four dimensions’. In this announcement we give a purely algebraic characterization of the 2-category of unframed unoriented 2-tangles in four 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.

2-tangle braided mondial 2-category. 

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • John C. Baez
    • 1
  • Laurel Langford
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaRiversideU.S.A. e-mail

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