Dehn surgery, rational open books and knot Floer homology

Details Dehn surgery, rational open books and knot Floer homology Dehn surgery, rational open books and knot Floer homology

2011-05-04

arxiv.org/abs/1105.0905v2

Mathematics

Geometric Topology

27 pages; a few typos corrected

Scientific paper

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.

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