Unstable Adams operations on p–local compact groups

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 $p^{m}$ to the group of unstable Adams operations on $G$ .

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Keywords

p-local compact group, unstable Adams operation, classifying space

Mathematical Subject Classification 2010

Primary: 55R35

Secondary: 55R40, 20D20

References

Publication

Received: 30 March 2011

Revised: 18 October 2011

Accepted: 22 October 2011

Published: 24 January 2012

Authors

Fabien Junod
Procter and Gamble 47, route de St-Georges Petit-Lancy CH-1213 Geneva Switzerland

Ran Levi
Institute of Mathematics University of Aberdeen Fraser Noble Building Aberdeen AB24 3UE UK

Assaf Libman
Institute of Mathematics University of Aberdeen Fraser Noble Building Aberdeen AB24 3UE UK

Volume 12, issue 1 (2012)

Fabien Junod, Ran Levi and Assaf Libman

Abstract