The cohomology ring of the GKM graph of a flag manifold of classical type

DOI10.1215/21562261-2693478zbMath1436.55012arXiv1104.1832OpenAlexW2014433520MaRDI QIDQ2258614

Yukiko Fukukawa, Mikiya Masuda, Hiroaki Ishida

Publication date: 26 February 2015

Published in: Kyoto Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.1832

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Equivariant homology and cohomology in algebraic topology (55N91) Homology and cohomology of homogeneous spaces of Lie groups (57T15)

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The torus equivariant cohomology rings of Springer varieties ⋮ The equivariant integral cohomology ring of the flag manifold of type C ⋮ A closed formula for the evaluation of foams ⋮ The equivariant cohomology rings of Peterson varieties ⋮ Upper bounds for the dimension of tori acting on GKM manifolds ⋮ The second cohomology of regular semisimple Hessenberg varieties from GKM theory ⋮ Cohomological non-rigidity of eight-dimensional complex projective towers

Cites Work

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• Torus graphs and simplicial posets
• Equivariant cohomology, Koszul duality, and the localization theorem
• 1-skeleta, Betti numbers, and equivariant cohomology
• A GKM description of the equivariant cohomology ring of a homogeneous space
• Computation of generalized equivariant cohomologies of Kac--Moody flag varieties