Lifting homotopy actions in rational homotopy theory
type: Item
instance of: scholarly article
title: Lifting homotopy actions in rational homotopy theory
zbMATH Open document ID: 0549.55008
DOI: 10.1016/0022-4049(84)90050-1
author: John Oprea
published in: Journal of Pure and Applied Algebra
publication date: 1984-01-01T00:00:00Z
review text: Es wird gezeigt, daß Homotopieaktionen auf ''hübschen'' Räumen X, das bedeutet hier: Homomorphismen \(\phi: G\to h-Aut(X)\), auf einem Raum \(\bar X_ 0\), der homotopie-äquivalent ist zur Rationalisierung \(X_ 0\) von X, zu einer strikten Operation geliftet werden können. Dies gilt für endliche Gruppen G und basiert auf dem Struktursatz für Automorphismen (bzw. Homotopie-Automorphismen) des minimalen Modells von \(X_ 0\). Des weiteren findet man Aussagen über Konjugiertheit und Verallgemeinerungen auf nicht diskrete Gruppen. Für diesen Zweck werden äquivariante minimale Modelle konstruiert.
Mathematics Subject Classification ID: 55P62
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 55P91
zbMATH DE Number: 3876205
zbMATH Keywords: homotopy actions on rational spaces
zbMATH Keywords: finite group actions
zbMATH Keywords: equivariant minimal models
MaRDI profile type: Publication
full work available at URL: 0022-4049(84)90050-1
OpenAlex ID: W1988688720
cites work: Q3942084
cites work: On 𝑃𝐿 de Rham theory and rational homotopy type
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cites work: Q5602064
cites work: Obstructions to homotopy equivalences
cites work: Fully Reducible Subgroups of Algebraic Groups
cites work: Galois Cohomology
cites work: Infinitesimal computations in topology
cites work: Equivariant Minimal Models
cites work: Applications of minimal simplicial groups
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description: scientific article; zbMATH DE number 3876205