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Knotted surfaces, braid movies, and beyond. (English) Zbl 0859.57027
Baez, John (ed.), Knots and quantum gravity. Proceedings of a workshop on knots and quantum gravity, held on May 14th-16th at the University of California at Riverside, CA (USA). Oxford: Clarendon Press (ISBN 0-19-853490-6/pbk). Oxford Lecture Series in Mathematics and its Applications 1, 191-229 (1994).
This is an extensive review on recent developments concerning diagrammatic ways to describe knotted surfaces embedded in 4-space. In Section 2, starting from work by Kamada and later extensions by the present authors a number of topological concepts and tools are described, such as surface braids, braid movies and braid movie moves. Section 3 reviews the authors’ diagrammatic methods for solving generalizations of the quantum Yang-Baxter equation. Section 4 interpretes work by Fischer to show how braid movies form a braided monoidal 2-category. Some new algebraic interpretations of braid movie moves are discussed in the final section.
For the entire collection see [Zbl 0796.00020].
Reviewer: W.Sarlet (Gent)

57Q45 Knots and links in high dimensions (PL-topology) (MSC2010)