Volume 13, issue 3 (2013)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Dehn surgery, rational open books and knot Floer homology

Matthew Hedden and Olga Plamenevskaya

Algebraic & Geometric Topology 13 (2013) 1815–1856
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.

Keywords
knots, rational open book, fibered, contact geometry, Floer homology, Dehn surgery
Mathematical Subject Classification 2010
Primary: 57M25, 57M27, 57R17, 57R58
References
Publication
Received: 8 May 2012
Revised: 13 October 2012
Accepted: 15 November 2012
Published: 21 May 2013
Authors
Matthew Hedden
Department of Math
Michigan State University
D325 WH
East Lansing, MI 48823
USA
http://www.math.msu.edu/~mhedden/Site/Home.html
Olga Plamenevskaya
Department of Mathematics
Stony Brook University
Stony Brook, NY 11794-3651
USA