Dehn surgery, rational open books and knot Floer homology

Hedden, Matthew; Plamenevskaya, Olga

doi:10.2140/agt.2013.13.1815

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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

DOI: 10.2140/agt.2013.13.1815

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

Volume 13, issue 3 (2013)