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Co-H-Spaces and Almost Localization

  • Cristina Costoya (a1) and Norio Iwase (a2)

Abstract

Apart from simply connected spaces, a non-simply connected co-H-space is a typical example of a space X with a coaction of 1 (X) along rX: X1 (X), the classifying map of the universal covering. If such a space X is actually a co-H-space, then the fibrewise p-localization of rX (or the ‘almost’ p-localization of X) is a fibrewise co-H-space (or an ‘almost’ co-H-space, respectively) for every prime p. In this paper, we show that the converse statement is true, i.e. for a non-simply connected space X with a coaction of 1 (X) along rX, X is a co-H-space if, for every prime p, the almost p-localization of X is an almost co-H-space.

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