Quantum and Floer cohomology have the same ring structure

Details Quantum and Floer cohomology have the same ring structure Quantum and Floer cohomology have the same ring structure

1994-01-26

arxiv.org/abs/hep-th/9401130v3

Physics

High Energy Physics

High Energy Physics - Theory

62 pages

Scientific paper

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.

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