Geometry & Topology

Ozsváth–Szabó invariants of contact surgeries

Marco Golla

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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
Received: 16 January 2013
Revised: 19 April 2014
Accepted: 9 May 2014
First available in Project Euclid: 16 November 2017

Permanent link to this document
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

Subjects
Primary: 57R17: Symplectic and contact topology
Secondary: 57R57: Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]

Keywords
tight contact structures Ozsváth–Szabó invariants

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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