Volume 19, issue 1 (2015)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Ozsváth–Szabó invariants of contact surgeries

Marco Golla

Geometry & Topology 19 (2015) 171–235
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.

Keywords
tight contact structures, Ozsváth–Szabó invariants
Mathematical Subject Classification 2010
Primary: 57R17
Secondary: 57R57
References
Publication
Received: 16 January 2013
Revised: 19 April 2014
Accepted: 9 May 2014
Published: 27 February 2015
Proposed: Peter S Ozsváth
Seconded: Yasha Eliashberg, Ciprian Manolescu
Authors
Marco Golla
Department of Mathematics
University of Pisa
Largo Bruno Pontecorvo 5
56127 Pisa
Italy