Document Type : Research Paper
College of Mathematics and Information Science, Hebei Normal University, Yuhua
Road 113, Shijiazhuang 050016, P. R. China
College of Mathematics and Information Science, Hebei Normal University, Yuhua Road 113, Shijiazhuang 050016, P. R. China
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.