Homotopy classification of higher homotopy commutative loop spaces with finitely generated cohomology

摘要

Suppose X is a simply connected mod p loop space such that the mod p cohomology H~*(X) is finitely generated as an algebra. We show that if X is a C_n-space in the sense of Williams then X is the total space of a C_n-fibration over a finite C_n-space. By using this result, we can reduce problems about C_n-spaces with finitely generated cohomology to the case of finite C_n-spaces. In particular, we give classification theorems for C_2-spaces and C_p-spaces with finitely generated cohomology.