On equivalence of Floer's and quantum cohomology

TL;DR

This paper proves that Floer cohomology and quantum cohomology rings of almost Kahler manifolds are isomorphic, using BRST trivial deformations, with an explicit example of the 3D flag space.

Contribution

It establishes the isomorphism between Floer and quantum cohomology rings via BRST trivial deformations, providing a nonperturbative proof and an explicit example.

Findings

Floer cohomology and quantum cohomology rings are isomorphic.

The isomorphism is shown using BRST trivial deformations.

Explicit computation for the 3D flag space Fl_3 confirms the theory.

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.