Algebraic & Geometric Topology

Unstable Adams operations on $p$–local compact groups

Fabien Junod, Ran Levi, and Assaf Libman

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A p–local compact group is an algebraic object modelled on the p–local homotopy theory of classifying spaces of compact Lie groups and p–compact groups. In the study of these objects unstable Adams operations are of fundamental importance. In this paper we define unstable Adams operations within the theory of p–local compact groups and show that such operations exist under rather mild conditions. More precisely, we prove that for a given p–local compact group G and a sufficiently large positive integer m, there exists an injective group homomorphism from the group of p–adic units which are congruent to 1 modulo pm to the group of unstable Adams operations on G.

Article information

Algebr. Geom. Topol., Volume 12, Number 1 (2012), 49-74.

Received: 30 March 2011
Revised: 18 October 2011
Accepted: 22 October 2011
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55R35: Classifying spaces of groups and $H$-spaces
Secondary: 55R40: Homology of classifying spaces, characteristic classes [See also 57Txx, 57R20] 20D20: Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure

p-local compact group unstable Adams operation classifying space


Junod, Fabien; Levi, Ran; Libman, Assaf. Unstable Adams operations on $p$–local compact groups. Algebr. Geom. Topol. 12 (2012), no. 1, 49--74. doi:10.2140/agt.2012.12.49.

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