Morse homology of nonsingular Morse-Smale foliations and its duality theorem

We define a Morse homology of the foliation which is defined by a general nonsingular Morse-Smale flow, applying the framework of the Conley index theory. In fact, we define a chain and a boundary homomorphism, therefore, a cochain and a cohomology are obtained as well. Furthermore, we prove a duality theorem on the homology and the cohomology.