Smooth toral actions
Given a smooth action of an elementary abelian group A on a smooth manifold M, the author describes the A-equivariant cohomology of M in terms of the equivariant cohomology of the singular strata provided the set of singular components satisfies a mild finiteness condition. Specifically, there is a filtration of the equivariant cohomology of M whose successive quotients are the equivariant cohomologies of the relevant singular sets. This decomposition yields a product decomposition for the Poincaré series of the equivariant cohomology of M. If the restriction map from equivariant to ordinary cohomology is surjective, then one recovers a result of Borel on the cohomology of the fixed set \(M^ A\), and in addition one obtains a relationship involving the Euler characteristics of M, \(M^ A\), and the intermediate strata of the group action.
smooth action of an elementary abelian group on a smooth manifold
product decomposition for the Poincaré series of the equivariant cohomology
scientific article; zbMATH DE number 3852045