# Unstable Adams operations on p-local compact groups

Fabien Junod, Ran Levi, Assaf Libman

Research output: Contribution to journalArticle

7 Citations (Scopus)

### Abstract

A $p$-local compact group is an algebraic object modeled 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 $\mathcal{G}$ 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 $\mathcal{G}$.
Original language English 49-74 26 Algebraic & Geometric Topology 12 1 31 Mar 2011 https://doi.org/10.2140/agt.2012.12.49 Published - 24 Jan 2012

### Fingerprint

Compact Group
Unstable
P-compact Group
Algebraic object
Classifying Space
Homotopy Theory
Compact Lie Group
Congruent
Injective
Homomorphism
Modulo
Unit
Integer

### Keywords

• classifying space
• p-local compact groups

### Cite this

In: Algebraic & Geometric Topology, Vol. 12, No. 1, 24.01.2012, p. 49-74.

Research output: Contribution to journalArticle

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