A Zp-index homomorphism for Zp-spaces

Let (X,T) be a Z(p)-space, that is, a topological space X equipped with a free action of the cyclic group Z(p), generated by a periodic homeo-morphism T:X -> X of period p. The goal of this paper is to construct a Z(p)-index graded homomorphism J:H, (X,T) -> Z(p) associated with (X,T), where H,(X,T) is the rth equivariant homology Z(p-)module of (X,T). Using this Zp-index we prove that, if (X,T) and (Y,S) are Z(p)-spaces and p = 2q with q odd, then, under certain homological conditions on X and Y, there is no equivariant map f : (X,T) -> (Y,S). This result includes the situation in which (Y,S) is the odd dimensional sphere S2n+1 equipped with the standard free periodic homeomorphism of period p = 2q with q odd. This is a special case of a result of T. Kobayashi [8].