Quantum cohomology of flag manifolds and Toda lattices
type: Item
instance of: scholarly article
title: Quantum cohomology of flag manifolds and Toda lattices
zbMATH Open document ID: 0828.55004
DOI: 10.1007/BF02101846
author: Bumsig Kim
author: Alexander Givental
published in: Communications in Mathematical Physics
publication date: 1995-07-26T00:00:00Z
full work available at URL: https://arxiv.org/abs/hep-th/9312096
review text: 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.
Mathematics Subject Classification ID: 55N35
Mathematics Subject Classification ID: 57R57
Mathematics Subject Classification ID: 81T99
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 778976
zbMATH Keywords: quantum cohomology of a compact Kaehler manifold
zbMATH Keywords: deformation of the cup product multiplication
zbMATH Keywords: Floer homology
zbMATH Keywords: equivariant quantum cohomology
zbMATH Keywords: flag manifolds
zbMATH Keywords: algebra of regular functions on an invariant Lagrangian variety of a Toda lattice
reviewed by: Vasile Oproiu
MaRDI profile type: Publication
arXiv ID: hep-th/9312096
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description: scientific article