Geometry & Topology

Stabilization in the braid groups II: Transversal simplicity of knots

Joan S Birman and William W Menasco

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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.

Article information

Geom. Topol., Volume 10, Number 3 (2006), 1425-1452.

Received: 24 June 2005
Accepted: 28 June 2006
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57M50: Geometric structures on low-dimensional manifolds 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)

contact structures tight transversal knot type 3-braids flypes Bennequin invariant transversally simple


Birman, Joan S; Menasco, William W. Stabilization in the braid groups II: Transversal simplicity of knots. Geom. Topol. 10 (2006), no. 3, 1425--1452. doi:10.2140/gt.2006.10.1425.

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