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Unstable Adams operations on $p$–local compact groups

Fabien Junod, Ran Levi and Assaf Libman

Algebraic & Geometric Topology 12 (2012) 49–74

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.

p-local compact group, unstable Adams operation, classifying space
Mathematical Subject Classification 2010
Primary: 55R35
Secondary: 55R40, 20D20
Received: 30 March 2011
Revised: 18 October 2011
Accepted: 22 October 2011
Published: 24 January 2012
Fabien Junod
Procter and Gamble
47, route de St-Georges
CH-1213 Geneva
Ran Levi
Institute of Mathematics
University of Aberdeen
Fraser Noble Building
AB24 3UE
Assaf Libman
Institute of Mathematics
University of Aberdeen
Fraser Noble Building
AB24 3UE