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Dehn surgery, rational open books and knot Floer homology

Matthew Hedden and Olga Plamenevskaya

Algebraic & Geometric Topology 13 (2013) 1815–1856

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.

knots, rational open book, fibered, contact geometry, Floer homology, Dehn surgery
Mathematical Subject Classification 2010
Primary: 57M25, 57M27, 57R17, 57R58
Received: 8 May 2012
Revised: 13 October 2012
Accepted: 15 November 2012
Published: 21 May 2013
Matthew Hedden
Department of Math
Michigan State University
D325 WH
East Lansing, MI 48823
Olga Plamenevskaya
Department of Mathematics
Stony Brook University
Stony Brook, NY 11794-3651