Quantum and Floer cohomology have the same ring structure

The action of the total cohomology H ∗ (M) of the almost Kahler manifold M on its Floer cohomology, int roduced originally by Floer, gives a new ring structure on H ∗ (M). We prove that the total cohomology space H ∗ (M), provided with this new ring structure, is isomorphic to the quantum cohomology ring. As a special case, we prove the the formula for the Floer cohomology ring of the complex grassmanians conjectured by Vafa and Witten CONTENTS