×

zbMATH — the first resource for mathematics

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)

MSC:
57Q45 Knots and links in high dimensions (PL-topology) (MSC2010)
PDF BibTeX XML Cite