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2017 Groups of unstable Adams operations on $p$–local compact groups
Ran Levi, Assaf Libman
Algebr. Geom. Topol. 17(1): 355-418 (2017). 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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Ran Levi. Assaf Libman. "Groups of unstable Adams operations on $p$–local compact groups." Algebr. Geom. Topol. 17 (1) 355 - 418, 2017. https://doi.org/10.2140/agt.2017.17.355

Information

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

zbMATH: 1361.55022
MathSciNet: MR3604380
Digital Object Identifier: 10.2140/agt.2017.17.355

Subjects:
Primary: 55R35
Secondary: 20D20

Rights: Copyright © 2017 Mathematical Sciences Publishers

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