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.
Citation
Matthew Hedden. Olga Plamenevskaya. "Dehn surgery, rational open books and knot Floer homology." Algebr. Geom. Topol. 13 (3) 1815 - 1856, 2013. https://doi.org/10.2140/agt.2013.13.1815
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