Algebraic & Geometric Topology 12 (2012) 49–74

DOI: 10.2140/agt.2012.12.49

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

Keywords

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

Mathematical Subject Classification

Primary: 55R35

Secondary: 20D20, 55R40

References

Publication

Received: 30 March 2011
Revised: 18 October 2011
Accepted: 22 October 2011
Published: 24 January 2012

Authors