Rational open books and Heegaard Floer contact invariants
Abstract: Giroux's correspondence between contact structures and open books
is of fundamental importance in 3-dimensional contact topology.
Rational open books, introduced by Baker-Etnyre-Van Horn-Morris,
are an extension of the classical notion. I will explain how to compute
the Ozsvath-Szabo contact invariants of contact 3-manifolds
given by rational open books, and discuss some applications.
In particular, our results yield tight contact structures on manifolds
obtained by large integral surgeries on certain knots.
(Joint with M. Hedden.)