TY - JOUR
T1 - The Milnor-stasheff filtration on spaces and generalized cyclic maps
AU - Iwase, Norio
AU - Mimura, Mamoru
AU - Oda, Nobuyuki
AU - Yoon, Yeon Soo
PY - 2012
Y1 - 2012
N2 - The concept of C k-spaces is introduced, situated at an intermediate stage between H-spaces and T-spaces. The C k-space corresponds to the k-th Milnor-Stasheff filtration on spaces. It is proved that a space X is a C k-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 C k-space are generalized to the C k-space for a map f : A → X. Projective spaces, lens spaces and spaces with a few cells are studied as examples ofC k-spaces, and non-C k-spaces.
AB - The concept of C k-spaces is introduced, situated at an intermediate stage between H-spaces and T-spaces. The C k-space corresponds to the k-th Milnor-Stasheff filtration on spaces. It is proved that a space X is a C k-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 C k-space are generalized to the C k-space for a map f : A → X. Projective spaces, lens spaces and spaces with a few cells are studied as examples ofC k-spaces, and non-C k-spaces.
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U2 - 10.4153/CMB-2011-130-8
DO - 10.4153/CMB-2011-130-8
M3 - Article
AN - SCOPUS:84865334961
VL - 55
SP - 523
EP - 536
JO - Canadian Mathematical Bulletin
JF - Canadian Mathematical Bulletin
SN - 0008-4395
IS - 3
ER -