Ozsváth-Szabó invariants of contact surgeries

Details Ozsváth-Szabó invariants of contact surgeries Ozsváth-Szabó invariants of contact surgeries

2012-01-25

arxiv.org/abs/1201.5286v1

Mathematics

Geometric Topology

48 pages, 15 figures

Scientific paper

We give new tightness criteria for positive surgeries along knots in the 3-sphere, generalising results of Lisca and Stipsicz, and Sahamie. The main tools will be Honda, Kazez and Matic's, Ozsvath and Szabo's Floer-theoretic contact invariants. We compute the Ozsvath and Szabo's invariant of positive contact surgeries along Legendrian knots in the 3-sphere in terms of the classical invariants of the knot. We also combine a Legendrian cabling construction with contact surgeries to get results about rational contact surgeries.

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