Stabilization in the braid groups II: Transversal simplicity of knots

Birman, Joan S; Menasco, William W

doi:10.2140/gt.2006.10.1425

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Stabilization in the braid groups II: Transversal simplicity of knots

Joan S Birman and William W Menasco

Geometry & Topology 10 (2006) 1425–1452

DOI: 10.2140/gt.2006.10.1425

arXiv: math.GT/0310280

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.

Keywords

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

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 57M50, 53C15

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Publication

Received: 24 June 2005

Accepted: 28 June 2006

Published: 4 October 2006

Proposed: Rob Kirby

Seconded: David Gabai, Cameron Gordon

Authors

Joan S Birman
Department of Mathematics Barnard College Columbia University 2990 Broadway New York, NY 10027 USA

William W Menasco
Department of Mathematics University at Buffalo Buffalo, NY 14260 USA

Volume 10, issue 3 (2006)