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2013 Power maps on $p$-regular Lie groups
Stephen Theriault
Homology Homotopy Appl. 15(2): 83-102 (2013).

Abstract

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 $\Omega\Sigma A$. We show that that complementary factor is very well behaved, and this allows us to deduce properties of $G$ from those of $\Omega\Sigma A$. 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.

Citation

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Stephen Theriault. "Power maps on $p$-regular Lie groups." Homology Homotopy Appl. 15 (2) 83 - 102, 2013.

Information

Published: 2013
First available in Project Euclid: 8 November 2013

zbMATH: 1280.55006
MathSciNet: MR3117388

Subjects:
Primary: 55P35
Secondary: 55T99

Keywords: $p$-regular , Lie group , power map

Rights: Copyright © 2013 International Press of Boston

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Vol.15 • No. 2 • 2013
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