Journal of Algebraic Combinatorics

, Volume 35, Issue 1, pp 19–59 | Cite as

Cohomology of GKM fiber bundles

  • Victor Guillemin
  • Silvia Sabatini
  • Catalin Zara


The equivariant cohomology ring of a GKM manifold is isomorphic to the cohomology ring of its GKM graph. In this paper we explore the implications of this fact for equivariant fiber bundles for which the total space and the base space are both GKM and derive a graph theoretical version of the Leray–Hirsch theorem. Then we apply this result to the equivariant cohomology theory of flag varieties.


Equivariant fiber bundle Equivariant cohomology GKM space Flag manifold 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Victor Guillemin
    • 1
  • Silvia Sabatini
    • 2
  • Catalin Zara
    • 3
  1. 1.Department of MathematicsMITCambridgeUSA
  2. 2.Department of MathematicsEPFLLausanneSwitzerland
  3. 3.Department of MathematicsUMass BostonBostonUSA

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