Equivariant cohomology and GKM-sheaves

Al-Jabea, Ibrahem (2018) Equivariant cohomology and GKM-sheaves. Masters thesis, Memorial University of Newfoundland.

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Abstract

If a topological group T acts on a topological space X, we may define the equivariant cohomology ring H*T(X). Due to its importance, several techniques have been developed to study equivariant cohomology. Goresky, Kottwitz, and MacPherson proved that of T torus action with a certain condition (GKM-manifold) the equivariant cohomology ring H*T(X) has a combinatorial description. More recently, T. Baird applied GKM-methods to general equivariantly formal compact T-manifold X. He developed a new class of sheaves (GKM-sheaves), and proved that the equivariant cohomology of X is isomorphic to the global sections of a GKM-sheaf FX. The purpose of this thesis is studying the GKM-theory and GKM-sheaves. In particular, we study the higher cohomology of GKM-sheaves and generalize the theory to compact T-manifolds for which H*T(X) is reflexive.

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