Fractional Dehn twists in knot theory and contact topology

Details Fractional Dehn twists in knot theory and contact topology Fractional Dehn twists in knot theory and contact topology

2012-01-25

arxiv.org/abs/1201.5290v2

Mathematics

Geometric Topology

33 pages,15 figures, version 2 updated references

Scientific paper

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. Applications are given 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.

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