Dehn surgery, rational open books and knot Floer homology

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.

27 pages; a few typos corrected; some corollaries removed and replaced by corollary about lens space surgeries

References in corpus (8)

• Knot Floer homology detects fibred knots
• Right-veering diffeomorphisms of compact surfaces with boundary II
• Lens space surgeries and L-space homology spheres
• Heegaard Floer homologies and contact structures
• The vanishing of the contact invariant in the presence of torsion
• Surgery diagrams for contact 3-manifolds
• Contact surgery and transverse invariants
• Heegaard Floer homology and Morse surgery

Cited by in corpus (4)

• $\tau$-invariants for knots in rational homology spheres
• A note on the knot Floer homology of fibered knots
• Null surgery on knots in L-spaces
• Stein-fillable open books of genus one that do not admit positive factorisations