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

Japanese
Authors.
Cristina Costoya and myself
Journal.
Proc. Edinb. Math. Soc., 58 (2015), 323-332.
Abstract.
Apart from simply-connected spaces, a non simply-connected co-H-space is a typical example of a space X with a co-action of Bπ1(X) along rX : X → Bπ1(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, resp.) 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 co-action of Bπ1(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.

Co-H-spaces and almost localization (adobe-pdf file, 385KB)