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Unstable Adams
operations on $p$–local compact groups
Fabien Junod, Ran Levi and Assaf Libman |
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Algebraic & Geometric Topology 12 (2012) 49–74
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Abstract |
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A –local compact group is an algebraic object modelled on the –local homotopy theory of classifying spaces of compact Lie groups and –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 –local compact groups and show that such operations exist under rather mild conditions. More precisely, we prove that for a given –local compact group and a sufficiently large positive integer , there exists an injective group homomorphism from the group of –adic units which are congruent to 1 modulo to the group of unstable Adams operations on . |
Keywords
p-local compact group, unstable Adams operation,
classifying space
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Mathematical Subject Classification 2010
Primary: 55R35
Secondary: 55R40, 20D20
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References |
Publication
Received: 30 March 2011
Revised: 18 October 2011
Accepted: 22 October 2011
Published: 24 January 2012
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Authors |
| Fabien Junod | |
| Procter and Gamble 47, route de St-Georges Petit-Lancy CH-1213 Geneva Switzerland |
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| Ran Levi | |
| Institute of Mathematics University of Aberdeen Fraser Noble Building Aberdeen AB24 3UE UK |
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| Assaf Libman | |
| Institute of Mathematics University of Aberdeen Fraser Noble Building Aberdeen AB24 3UE UK |
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