The Milnor–Stasheff Filtration on Spaces and Generalized Cyclic Maps

Abstract

AbstractThe concept of Ck-spaces is introduced, situated at an intermediate stage between H-spaces and T-spaces. The Ck-space corresponds to the k-th Milnor–Stasheff filtration on spaces. It is proved that a space X is a Ck-space if and only if the Gottlieb set G(Z, X) = [Z, X] for any space Z with cat Z ≤ k, which generalizes the fact that X is a T-space if and only if G(ΣB, X) = [ΣB, X] for any space B. Some results on the Ck-space are generalized to the -space for a map ƒ : A → X. Projective spaces, lens spaces and spaces with a few cells are studied as examples of Ck-spaces, and non-Ck-spaces.