English

Dehn surgery, rational open books and knot Floer homology

Geometric Topology 2015-03-19 v3 Symplectic Geometry

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.

Keywords

Cite

@article{arxiv.1105.0905,
  title  = {Dehn surgery, rational open books and knot Floer homology},
  author = {Matthew Hedden and Olga Plamenevskaya},
  journal= {arXiv preprint arXiv:1105.0905},
  year   = {2015}
}

Comments

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