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Stabilization in the braid groups. II. Transversal simplicity of knots. (English) Zbl 1130.57005

Summary: The main result of this paper is a negative answer to the question: are all transversal knot types transversally simple? An explicit infinite family of examples is given of closed 3-braids that define transversal knot types that are not transversally simple. The method of proof is topological and indirect.
For part I of the paper see Geom. Topol. 19, 413–540 (2006; Zbl 1128.57003).

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
57M50 General geometric structures on low-dimensional manifolds
57R17 Symplectic and contact topology in high or arbitrary dimension

Citations:

Zbl 1128.57003
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References:

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