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Co-H-Spaces and Almost Localization

Part of: Homotopy theory Fiber spaces and bundles

Published online by Cambridge University Press:  24 October 2014

Cristina Costoya  and
Norio Iwase
Cristina Costoya
Affiliation:
Departamento de Computatión, Álxebra, Universidade da Coruña, Campus Elviña, 15071 A Coruña, Spain, (cristina.costoya@udc.es)
Norio Iwase
Affiliation:
Faculty of Mathematics, Kyushu University, Fukuoka 810-8560, Japan, (iwase@math.kyushu-u.ac.jp)
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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 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, 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 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.

Keywords

co-H-spacefibrewise localizationLusternik—Schnirelmann categoryLS category

MSC classification

Primary: 55P45: $H$-spaces and duals
Secondary: 55R70: Fibrewise topology 55P60: Localization and completion
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 58 , Issue 2 , June 2015 , pp. 323 - 332
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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