Ozsváth-Szabó invariants of contact surgeries

Abstract

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.

55 pages, 15 figures; some references have been updated, and the exposition has been improved

References in corpus (5)

• On the equivalence of Legendrian and transverse invariants in knot Floer homology
• Knot concordance and homology cobordism
• Legendrian and transverse cables of positive torus knots
• Dehn Twists in Heegaard Floer Homology
• Contact surgery and transverse invariants

Cited by in corpus (3)

• Sutured Floer homology and invariants of Legendrian and transverse knots
• Maximal Thurston-Bennequin number and reducible Legendrian surgery
• On contact surgery and knot Floer invariants