Applications of group actions on finite complexes to Hilbert cube manifolds

Abstract

For any compact Hilbert cube manifold M such that H ~ ∗ ( M , Z p ) {\tilde H_\ast }(M,{Z_p}) , there exists an embedding g of M into the Hilbert cube Q such that g ( M ) g(M) is the fixed point set of a semifree periodic homeomorphism of Q with period p. A counterexample is given to the conjecture that any two proper homotopic period p homeomorphisms of a Hilbert cube manifold such that the homeomorphisms revolve trivially about a unique fixed point are equivalent. A counterexample is also given for the case where the fixed point set is empty.