Discrete models for the \(p\)-local homotopy theory of compact Lie groups and \(p\)-compact groups
type: Item
instance of: scholarly article
title: Discrete models for the \(p\)-local homotopy theory of compact Lie groups and \(p\)-compact groups
zbMATH Open document ID: 1135.55008
author: Carles Broto
author: Ran Levi
author: Bob Oliver
published in: Geometry \& Topology
publication date: 2007-03-21T00:00:00Z
review text: The \(p\)-completed classifying spaces of finite and compact Lie groups, together with classifying spaces of \(p\)-compact groups share many similar homotopy theoretic properties. Despite these similarities the techniques used to derive them are different in each case. The aim of this paper is to provide a framework in which these similar results a derived from the common framework. The key idea is to replace fusion systems over finite \(p\)-groups with fusion systems over discrete \(p\)-toral groups. A \(p\)-toral group being a group that contains a \(p\)-torus (a group of the form \(({\mathbb Z}/p^{\infty})^{r}\) for some \(r \geq 0\)) as a normal subgroup of \(p\)-power index. The fusion system describes the way in which the various subgroups of a \(p\)-toral group fit together. In developing this theory of fusions systems the authors show how to define the classifying spaces in ways that include the Lie case and the discrete group case.
Mathematics Subject Classification ID: 55R35
Mathematics Subject Classification ID: 55R40
Mathematics Subject Classification ID: 57T10
zbMATH DE Number: 5136063
zbMATH Keywords: \(p\)-toral group
zbMATH Keywords: \(p\)-compact group
zbMATH Keywords: fusion systems
zbMATH Keywords: Sylow subgroup
zbMATH Keywords: orbit category
Wikidata QID: Q115231053
reviewed by: Jonathan Hodgson
MaRDI profile type: Publication
full work available at URL: gt.2007.11.315
OpenAlex ID: W2158483385
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DOI: 10.2140/GT.2007.11.315
description: scientific article; zbMATH DE number 5136063