Dehn surgery, rational open books and knot Floer homology

Matthew Hedden; Olga Plamenevskaya

doi:10.2140/agt.2013.13.1815

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arXiv · 1105.0905

Dehn surgery, rational open books and knot Floer homology

Matthew Hedden·Olga Plamenevskaya

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Abstract

By recent results of Baker--Etnyre--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. Possible applications to lens space surgeries are discussed.

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Matthew Hedden, Olga Plamenevskaya. 2012-05-08. Dehn surgery, rational open books and knot Floer homology. https://doi.org/10.2140/agt.2013.13.1815

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