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

Article 30, Volume 38, Number 2, July 2012, Page 529-542  XML PDF (229 K)
Document Type: Research Paper
Authors
1Yanchang Chen; 2Yanying Wang
1College of Mathematics and Information Science, Hebei Normal University, Yuhua Road 113, Shijiazhuang 050016, P. R. China
2College of Mathematics and Information Science, Hebei Normal University, Yuhua Road 113, Shijiazhuang 050016, P. R. China
Abstract
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.
Keywords
G-manifold; equivariant index; equivariant cohomology; ring homomorphism
Main Subjects
55-XX Algebraic topology; 57-XX Manifolds and cell complexes; 58-XX Global analysis, analysis on manifolds
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