Algebraic & Geometric Topology

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

Ran Levi and Assaf Libman

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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
Received: 20 December 2015
Revised: 3 June 2016
Accepted: 17 June 2016
First available in Project Euclid: 16 November 2017

Permanent link to this document
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

Subjects
Primary: 55R35: Classifying spaces of groups and $H$-spaces
Secondary: 20D20: Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure

Keywords
$p$–local compact groups unstable Adams operations

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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