TY - JOUR

T1 - Co-H-Spaces and Almost Localization

AU - Costoya, Cristina

AU - Iwase, Norio

N1 - Publisher Copyright:
Copyright © Edinburgh Mathematical Society 2014.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 2014/10/27

Y1 - 2014/10/27

N2 - Apart from simply connected spaces, a non-simply connected co-H-space is a typical example of a space X with a coaction of Bπ 1 (X) along rX : X → Bπ 1 (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 Bπ 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.

AB - Apart from simply connected spaces, a non-simply connected co-H-space is a typical example of a space X with a coaction of Bπ 1 (X) along rX : X → Bπ 1 (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 Bπ 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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U2 - 10.1017/S0013091514000078

DO - 10.1017/S0013091514000078

M3 - Article

AN - SCOPUS:84945448618

VL - 58

SP - 323

EP - 332

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

IS - 2

ER -