On the homology of a fixed point set

Abstract

The objects to be studied are the continuous functions of the sort glXXT->X. Here X is an ANR(ikf) (for metric spaces) such as a manifold or function space, and T is any normal Hausdorff space, but which in nature would be acyclic [ll], or a semigroup For an open subset 0 of XX T define & fixed point of g\ 0 to be a point x such that there exists (x, t) in 0 which is a solution to g(x f t) =x. The closure of the set of fixed points of g\ 0 is Fix g\ 0, and the set of solutions (x, t) in 0 is S(g\ 0). It will generally be assumed that the closure of g( These conditions will be signaled by the terminology "g is nondegenerate on 0." Then there is a homomorphism induced by g }