Norio Iwase
Mailing Adress: Faculty of Mathematics, Kyushu University, Motooka 744, Fukuoka 819-0395, Japan
E-mail Adress: iwase_AT__AT_math.kyushu-u.ac.jp
Authors.
Myself, M.Mimura, N. Oda and Y.S. Yoon
Journal.
Canadian Mathematical Bulletin, 55 (2012), 523-536.
Abstract.
The 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 Ckf-space for a map f : A → X. Projective spaces, lens spaces and spaces with a few cells are studied as examples of Ck-spaces, and non-Ck-spaces.
- The Milnor-Stasheff Filtration on Spaces and Generalized Cyclic Maps (postscript file, 203.9 Kbytes)