Ciocan-Fontanine, Ionuţ Quantum cohomology of flag varieties. (English) Zbl 0847.14011 Int. Math. Res. Not. 1995, No. 6, 263-277 (1995). The quantum cohomology ring of a Kähler manifold is a deformation of the usual cohomology ring introduced by E. Witten [Commun. Math. Phys. 118, No. 3, 411-449 (1988; Zbl 0674.58047)]. The computation of a quantum cohomology ring is generally a difficult task. Givental’ and Kim proposed a presentation of the quantum cohomology rings in the case of flag varieties. In the paper under review a method for computing these rings is described and the presentation proposed by Givental’ and Kim is established. It is observed that this same method should also apply to more general homogeneous spaces. Reviewer: N.Andruskiewitsch (Córdoba) Cited in 3 ReviewsCited in 23 Documents MSC: 14F99 (Co)homology theory in algebraic geometry 14M15 Grassmannians, Schubert varieties, flag manifolds 81T10 Model quantum field theories 32Q15 Kähler manifolds Keywords:quantum cohomology ring; flag varieties Citations:Zbl 0674.58047 PDFBibTeX XMLCite \textit{I. Ciocan-Fontanine}, Int. Math. Res. Not. 1995, No. 6, 263--277 (1995; Zbl 0847.14011) Full Text: DOI arXiv