  In this paper we construct a Floer-homology invariant for a natural and wide
class of sutured manifolds that we call balanced. This generalizes the Heegaard
Floer hat theory of closed three-manifolds and links. Our invariant is
unchanged under product decompositions and is zero for nontaut sutured
manifolds. As an application, an invariant of Seifert surfaces is given and is
computed in a few interesting cases.
