an:04034682
Zbl 0635.57020
May, J. P.
A generalization of Smith theory
EN
Proc. Am. Math. Soc. 101, 728-730 (1987).
00152674
1987
j
57S17 55M35 55N25
finite p-group; finite dimensional G-CW-complex; subcomplex of singular points; Bredon equivariant cohomology groups
Let G be a finite p-group and let X be a finite dimensional G-CW-complex with finite dimensional mod p-cohomology. Let SX denote the subcomplex of singular points X and let \(FX:=X/SX\). The author found some inequalities which involve dimensions of the mod p-cohomology groups of X, SX and FX/G. His inequalities are sharper than those which can be obtained from the classical P. A. Smith theory. The proofs are based on an interpretation of the (ordinary) cohomology groups of X, SX and FX/G as Bredon equivariant cohomology groups of X with coefficients in suitable systems.
S.Jackowski