Equivariant cohomology and GKM-sheaves

Abstract

If a topological group T acts on a topological space X, we may define the equivariant cohomology ring HT(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 HT(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.