Quantum and Floer cohomology have the same ring structure

Abstract

The action of the total cohomology $H^{\ast }(M)$ of the almost Kahler manifold $M$ on its Floer cohomology, int roduced originally by Floer, gives a new ring structure on $H^{\ast }(M)$. We prove that the total cohomology space $H^{\ast }(M)$, 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.

62 pages

References in corpus (6)

• Topological Field Theory and Rational Curves
• The Verlinde Algebra And The Cohomology Of The Grassmannian
• Quantum cohomology of partial flag manifolds
• Degree of the generalized Plücker embedding of a Quot scheme and Quantum cohomology
• On Quantum Cohomology Rings of Fano Manifolds and a Formula of Vafa and Intriligator
• Towards a Schubert calculus for maps from a Riemann surface to a Grassmannian

Cited by in corpus (4)

• Degree of the generalized Plücker embedding of a Quot scheme and Quantum cohomology
• Spectral invariants with bulk, quasimorphisms and Lagrangian Floer theory
• Painleve' transcendents and two-dimensional topological field theory
• Products and relations in symplectic Floer homology