Dehn surgery, rational open books and knot Floer homology

Hedden, Matthew¹ ; Plamenevskaya, Olga²

¹Department of Math, Michigan State University, D325 WH, East Lansing, MI 48823, USA
²Department of Mathematics, Stony Brook University, Stony Brook, NY 11794-3651, USA

Algebraic and Geometric Topology, Tome 13 (2013) no. 3, pp. 1815-1856

Résumé

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.

Détail

DOI : 10.2140/agt.2013.13.1815

Classification : 57M25, 57M27, 57R17, 57R58
Keywords: knots, rational open book, fibered, contact geometry, Floer homology, Dehn surgery

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