On equivalence of Floer's and quantum cohomology

Abstract

(In the revised version the relevant aspect of noncompactness of the moduli of instantons is discussed. It is shown nonperturbatively that any BRST trivial deformation of A-model which does not change the ranks of BRST cohomology does not change the topological correlation functions either) We show that the Floer cohomology and quantum cohomology rings of the almost Kahler manifold M, both defined over the Novikov ring of the loop space LM of M, are isomorphic. We do it using a BRST trivial deformation of the topological A-model. As an example we compute the Floer = quantum cohomology of the 3-dimensional flag space Fl_3.