## Geometry & Topology

### Ozsváth–Szabó invariants of contact surgeries

Marco Golla

#### 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 Matić’s, and Ozsváth and Szabó’s Floer-theoretic contact invariants. We compute Ozsváth–Szabó contact 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.

#### Article information

Source
Geom. Topol., Volume 19, Number 1 (2015), 171-235.

Dates
Revised: 19 April 2014
Accepted: 9 May 2014
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.gt/1510858679

Digital Object Identifier
doi:10.2140/gt.2015.19.171

Mathematical Reviews number (MathSciNet)
MR3318750

Zentralblatt MATH identifier
1310.57040

#### Citation

Golla, Marco. Ozsváth–Szabó invariants of contact surgeries. Geom. Topol. 19 (2015), no. 1, 171--235. doi:10.2140/gt.2015.19.171. https://projecteuclid.org/euclid.gt/1510858679

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