Quantum Cohomology And All That

Abstract

We found a quantum cohomology/homology of quantum Hall effect which arises as the invariant property of the Chern-Simons theory of quantum Hall effect and showed that it should be equivalent to the quantum cohomology which arose as the invariant property of topological sigma models. This isomorphism should be related with an equivalence between the supersymmetric- and quantization structures in two dimensional models and/or with an equivalence between topological sigma models and the Chern-Simons theory by the methode of master equation.