Equivariant Cohomology and Analytic Descriptions of Ring Isomorphisms
نویسندگان
چکیده
In this paper we consider a class of connected closed G-manifolds with a non-empty finite fixed point set, each M of which is totally non-homologous to zero in MG (or G-equivariantly formal), where G = Z2. With the help of the equivariant index, we give an explicit description of the equivariant cohomology of such a G-manifold in terms of algebra, so that we can obtain analytic descriptions of ring isomorphisms among equivariant cohomology rings of such G-manifolds, and a necessary and sufficient condition that the equivariant cohomology rings of such two G-manifolds are isomorphic. This also leads us to analyze how many there are equivariant cohomology rings up to isomorphism for such G-manifolds in 2and 3-dimensional cases.
منابع مشابه
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