Geodesic
Power maps on $p$-regular Lie groups
Homology, homotopy, and applications, Tome 15 (2013) no. 2, pp. 83-102.

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

A simple, simply-connected, compact Lie group $G$ is $p$-regular if it is homotopy equivalent to a product of spheres when localized at $p$. If $A$ is the corresponding wedge of spheres, then it is well known that there is a p-local retraction of $G$ off $ΩΣA$. We show that that complementary factor is very well behaved, and this allows us to deduce properties of $G$ from those of $ΩΣA$. We apply this to show that, localized at $p$, the $p^{th}$-power map on $G$ is an $H$-map. This is a significant step forward in Arkowitz-Curjel and McGibbon’s programme for identifying which power maps between finite $H$-spaces are $H$-maps.
DOI : 10.4310/HHA.2013.v15.n2.a5
Classification : 55Txx, 55P35
Keywords: Lie group, $p$-regular, power map 
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     author = {Stephen Theriault},
     title = {Power maps on $p$-regular {Lie} groups},
     journal = {Homology, homotopy, and applications},
     pages = {83--102},
     publisher = {mathdoc},
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     number = {2},
     year = {2013},
     doi = {10.4310/HHA.2013.v15.n2.a5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2013.v15.n2.a5/}
}
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Stephen Theriault. Power maps on $p$-regular Lie groups. Homology, homotopy, and applications, Tome 15 (2013) no. 2, pp. 83-102. doi : 10.4310/HHA.2013.v15.n2.a5. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2013.v15.n2.a5/

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