ring structures of mod p equivariant cohomology rings and ring homomorphisms between them

in this paper, we consider a class of connected oriented (with respect to z/p) closed g-manifolds with a non-empty finite fixed point set, each of which is g-equivariantly formal, where g = z/p and p is an odd prime. using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a g-manifold in terms of algebra. this makes it possible to determine the number of equivariant cohomology rings (up to isomorphism) of such 2-dimensional g-manifolds. moreover, we obtain a description of the ring homomorphism between equivariant cohomology rings of such two g-manifolds induced by a g-equivariant map, and show a characterization of the ring homomorphism.