Algebraic & Geometric Topology

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

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.

Article information

Source
Algebr. Geom. Topol., Volume 17, Number 1 (2017), 355-418.

Dates
Revised: 3 June 2016
Accepted: 17 June 2016
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.agt/1510841316

Digital Object Identifier
doi:10.2140/agt.2017.17.355

Mathematical Reviews number (MathSciNet)
MR3604380

Zentralblatt MATH identifier
1361.55022

Citation

Levi, Ran; Libman, Assaf. Groups of unstable Adams operations on $p$–local compact groups. Algebr. Geom. Topol. 17 (2017), no. 1, 355--418. doi:10.2140/agt.2017.17.355. https://projecteuclid.org/euclid.agt/1510841316

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