Unstable Adams operations on p–local compact groups

Junod, Fabien¹ ; Levi, Ran² ; Libman, Assaf²

¹Procter and Gamble, 47, route de St-Georges, Petit-Lancy, CH-1213 Geneva, Switzerland
²Institute of Mathematics, University of Aberdeen, Fraser Noble Building, Aberdeen, AB24 3UE, UK

Algebraic and Geometric Topology, Tome 12 (2012) no. 1, pp. 49-74

Résumé

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.

Détail

DOI : 10.2140/agt.2012.12.49

Classification : 55R35, 55R40, 20D20
Keywords: p-local compact group, unstable Adams operation, classifying space

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