Volume 13, issue 6 (2013)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Fractional Dehn twists in knot theory and contact topology

William H Kazez and Rachel Roberts

Algebraic & Geometric Topology 13 (2013) 3603–3637
Abstract

Fractional Dehn twists give a measure of the difference between the relative isotopy class of a homeomorphism of a bordered surface and the Thurston representative of its free isotopy class. We show how to estimate and compute these invariants. We discuss the relationship of our work to stabilization problems in classical knot theory, general open book decompositions and contact topology. We include an elementary characterization of overtwistedness for contact structures described by open book decompositions.

Keywords
fractional Dehn twist, overtwisted, contact structure, open book decomposition, fibred link, surface automorphism
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 53D10
References
Publication
Received: 27 September 2012
Revised: 7 February 2013
Accepted: 6 June 2013
Published: 14 October 2013
Authors
William H Kazez
Department of Mathematics
University of Georgia
Athens, GA 30602
USA
Rachel Roberts
Department of Mathematics
Washington University
St Louis, MO 63130
USA