Algebraic & Geometric Topology

Dehn surgery, rational open books and knot Floer homology

Matthew Hedden and Olga Plamenevskaya

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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

knots rational open book fibered contact geometry Floer homology Dehn surgery


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.

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