Volume 10, issue 3 (2006)

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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

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