## Quantum cohomology of flag manifolds and Toda lattices.(English)Zbl 0828.55004

The quantum cohomology $$QH^* (X)$$ of a compact Kaehler manifold $$X$$ is a certain deformation of the cup product multiplication in the ordinary cohomology of $$X$$. The authors study the relation of the quantum cohomology with the Floer homology and introduce the equivariant quantum cohomology. Then they compute the quantum cohomology algebras of the flag manifolds showing that it does coincide with the algebra of regular functions on an invariant Lagrangian variety of a Toda lattice.
Reviewer: V.Oproiu (Iaşi)

### MSC:

 55N35 Other homology theories in algebraic topology 57R57 Applications of global analysis to structures on manifolds 81T99 Quantum field theory; related classical field theories 37-XX Dynamical systems and ergodic theory
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### References:

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