Quantum cohomology of flag manifolds and Toda lattices
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.
quantum cohomology of a compact Kaehler manifold
deformation of the cup product multiplication
algebra of regular functions on an invariant Lagrangian variety of a Toda lattice
scientific article