Geodesic
On the 2-adic $K$-localizations of $H$-spaces
Homology, homotopy, and applications, Tome 9 (2007) no. 1, pp. 331-366.

Voir la notice de l'article provenant de la source International Press of Boston

We determine the 2-adic $K$-localizations for a large class of $H$-spaces and related spaces. As in the odd primary case, these localizations are expressed as fibers of maps between specified infinite loop spaces, allowing us to approach the 2-primary $v_1$-periodic homotopy groups of our spaces. The present $v_1$-periodic results have been applied very successfully to simply-connected compact Lie groups by Davis, using knowledge of the complex, real, and quaternionic representations of the groups. We also functorially determine the united 2-adic $K$-cohomology algebras (including the 2-adic $KO$-cohomology algebras) for all simply-connected compact Lie groups in terms of their representation theories, and we show the existence of spaces realizing a wide class of united 2-adic $K$-cohomology algebras with specified operations.
DOI : 10.4310/HHA.2007.v9.n1.a14
Classification : 55N15, 55P60, 55Q51, 55S25
Keywords: $K$-localizations, $v_1$-periodic homotopy, 2-adic $K$-theory, united $K$-theory, compact Lie groups 
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     author = {A. K. Bousfield},
     title = {On the 2-adic $K$-localizations of $H$-spaces},
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     pages = {331--366},
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     year = {2007},
     doi = {10.4310/HHA.2007.v9.n1.a14},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2007.v9.n1.a14/}
}
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A. K. Bousfield. On the 2-adic $K$-localizations of $H$-spaces. Homology, homotopy, and applications, Tome 9 (2007) no. 1, pp. 331-366. doi : 10.4310/HHA.2007.v9.n1.a14. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2007.v9.n1.a14/

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