Cohomology of GKM Fiber Bundles

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Guillemin, Victor
Sabatini, Silvia
Zara, Catalin
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Abstract
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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.
Comment: The paper has been accepted by the Journal of Algebraic Combinatorics. The final publication is available at springerlink.com
Keywords
Mathematics - Combinatorics, Mathematics - Differential Geometry, 55R91, 05C25, 05E15, 55N91
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