Groups of unstable Adams operations on p–local compact groups

Levi, Ran; Libman, Assaf

doi:10.2140/agt.2017.17.355

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Groups of unstable Adams operations on $p$–local compact groups

Ran Levi and Assaf Libman

Algebraic & Geometric Topology 17 (2017) 355–418

DOI: 10.2140/agt.2017.17.355

Abstract

A $p$ –local compact group is an algebraic object modelled on the homotopy theory associated with $p$ –completed classifying spaces of compact Lie groups and $p$ –compact groups. In particular $p$ –local compact groups give a unified framework in which one may study $p$ –completed classifying spaces from an algebraic and homotopy theoretic point of view. Like connected compact Lie groups and $p$ –compact groups, $p$ –local compact groups admit unstable Adams operations: self equivalences that are characterised by their cohomological effect. Unstable Adams operations on $p$ –local compact groups were constructed in a previous paper by F Junod, R Levi, and A Libman. In the present paper we study groups of unstable operations from a geometric and algebraic point of view. We give a precise description of the relationship between algebraic and geometric operations, and show that under some conditions, unstable Adams operations are determined by their degree. We also examine a particularly well behaved subgroup of unstable Adams operations.

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Keywords

$p$–local compact groups, unstable Adams operations

Mathematical Subject Classification 2010

Primary: 55R35

Secondary: 20D20

References

Publication

Received: 20 December 2015

Revised: 3 June 2016

Accepted: 17 June 2016

Published: 26 January 2017

Authors

Ran Levi
Institute of Mathematics University of Aberdeen Fraser Noble Building 138 Aberdeen AB24 3UE United Kingdom

Assaf Libman

Volume 17, issue 1 (2017)