## Algebraic & Geometric Topology

### Unstable Adams operations on $p$–local compact groups

#### Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715331

Digital Object Identifier
doi:10.2140/agt.2012.12.49

Mathematical Reviews number (MathSciNet)
MR2889545

Zentralblatt MATH identifier
1258.55010

#### Citation

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. https://projecteuclid.org/euclid.agt/1513715331

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