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Fractional Dehn twists give a measure of the difference between the relativeisotopy class of a homeomorphism of a bordered surface and the Thurstonrepresentative of its free isotopy class. We show how to estimate and computethese invariants. We discuss the the relationship of our work to stabilizationproblems in classical knot theory, general open book decompositions, andcontact topology. We include an elementary characterization of overtwistednessfor contact structures described by open book decompositions.

Fractional Dehn twists in knot theory and contact topology