Algebraic & Geometric Topology

Dehn surgery, rational open books and knot Floer homology

Matthew Hedden and Olga Plamenevskaya

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Abstract

By recent results of Baker, Etnyre and Van Horn-Morris, a rational open book decomposition defines a compatible contact structure. We show that the Heegaard Floer contact invariant of such a contact structure can be computed in terms of the knot Floer homology of its (rationally null-homologous) binding. We then use this description of contact invariants, together with a formula for the knot Floer homology of the core of a surgery solid torus, to show that certain manifolds obtained by surgeries on bindings of open books carry tight contact structures.

Article information

Source
Algebr. Geom. Topol., Volume 13, Number 3 (2013), 1815-1856.

Dates
Received: 8 May 2012
Revised: 13 October 2012
Accepted: 15 November 2012
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715601

Digital Object Identifier
doi:10.2140/agt.2013.13.1815

Mathematical Reviews number (MathSciNet)
MR3071144

Zentralblatt MATH identifier
1336.57009

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds 57R17: Symplectic and contact topology 57R58: Floer homology

Keywords
knots rational open book fibered contact geometry Floer homology Dehn surgery

Citation

Hedden, Matthew; Plamenevskaya, Olga. Dehn surgery, rational open books and knot Floer homology. Algebr. Geom. Topol. 13 (2013), no. 3, 1815--1856. doi:10.2140/agt.2013.13.1815. https://projecteuclid.org/euclid.agt/1513715601


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