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Knot diagrams and braid theories in dimension 4. (English) Zbl 0849.57022
Marar, W. L. (ed.), Real and complex singularities. Papers from the 3rd international workshop held Aug. 1-5, 1994 in São Carlos, Brazil. Harlow: Longman. Pitman Res. Notes Math. Ser. 333, 112-147 (1995).
In knot theory, a knot or link is usually described by a diagram, which is a projected image on a plane equipped with over/under information at each crossing. Most of the known knot invariants can be defined and computed via diagrams. The authors study knotted surfaces in 4-space via “diagrams” in various points of view.
The paper gives a summary of diagrammatic method to investigate knotted surfaces. In Section 2, Roseman moves (fundamental moves to surface diagrams in 3-space) and Carter-Saito moves (moves to movies) are introduced. In Section 3, 2-dimensional braid theory is treated. Section 4 concerns generalizations of Yang-Baxter equation.
For the entire collection see [Zbl 0827.00040].
Reviewer: T.Kanenobu (Osaka)

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