The Heegaard-Floer complex associated with the sutured manifolds

Sutured manifolds were first introduced by Gabai in his study of taut foliations on
three-manifolds with toridal boundary. Juhasz, building on the theory developed by
Ozsvath and Szabo, assigned a chain complex to (a Heegaard diagram for) a
sutured manifold whose corresponding homology group gives an invariant with
several nice  applications. In this talk, after covering some of the basic definitions,
constructions and results, I will present a joint work with Akram Alishahi, in which
we refine the construction of Juhasz. The knot and link Floer complexes, in their full
form, are recovered as special cases as well.