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 cohom...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.Read More
Publication Year: 2018
Publication Date: 2018-05-01
Language: en
Type: dissertation
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