Geometry & Topology

Stabilization in the braid groups II: Transversal simplicity of knots

Joan S Birman and William W Menasco

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513799772

Digital Object Identifier
doi:10.2140/gt.2006.10.1425

Mathematical Reviews number (MathSciNet)
MR2255503

Zentralblatt MATH identifier
1130.57005

Subjects
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.)

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

Citation

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. https://projecteuclid.org/euclid.gt/1513799772


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