Fractional Dehn twists in knot theory and contact topology

Kazez, William H; Roberts, Rachel

doi:10.2140/agt.2013.13.3603

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Fractional Dehn twists in knot theory and contact topology

William H Kazez and Rachel Roberts

Algebraic & Geometric Topology 13 (2013) 3603–3637

DOI: 10.2140/agt.2013.13.3603

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

Volume 13, issue 6 (2013)