Fractional Dehn twists in knot theory and contact topology

Kazez, William H¹ ; Roberts, Rachel²

¹Department of Mathematics, University of Georgia, Athens, GA 30602, USA
²Department of Mathematics, Washington University, St Louis, MO 63130, USA

Algebraic and Geometric Topology, Tome 13 (2013) no. 6, pp. 3603-3637

Résumé

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.

Détail

DOI : 10.2140/agt.2013.13.3603

Classification : 57M50, 53D10
Keywords: fractional Dehn twist, overtwisted, contact structure, open book decomposition, fibred link, surface automorphism

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