Equivariant rational homotopy theory as a closed model category
type: Item
instance of: scholarly article
title: Equivariant rational homotopy theory as a closed model category
zbMATH Open document ID: 0929.55012
DOI: 10.1016/S0022-4049(97)00127-8
published in: Journal of Pure and Applied Algebra
publication date: 2000-01-25T00:00:00Z
review text: Using the result of \textit{D. A. Edwards} and \textit{H. M. Hastings} [Čech and Steenrod homotopy theories with applications to geometric topology, Lect. Notes Math. 542 (1976; Zbl 0334.55001)] the author proves that a closed model structure on a category \({\mathcal C}\) can be extended to the functor category \({\mathcal I}\)-\({\mathcal C}\) where the morphisms of the category \({\mathcal I}\) are isomorphisms. For a finite group \(G\), \({\mathcal I}\) denotes the category of the canonical orbits and \({\mathcal C}\) is the category of commutative differential graded algebras. So that the result of \textit{B. L. Fine} and \textit{G. Triantafillou} [Can. J. Math. 45, No. 6, 1200-1210 (1993; Zbl 0805.55009)] can be reproved.
Mathematics Subject Classification ID: 55P62
Mathematics Subject Classification ID: 18G30
Mathematics Subject Classification ID: 55P60
Mathematics Subject Classification ID: 55P91
Mathematics Subject Classification ID: 55U35
zbMATH DE Number: 1308282
zbMATH Keywords: model category
zbMATH Keywords: Sullivan models
author: Marek Golasiński
reviewed by: Jean-Claude Thomas
MaRDI profile type: Publication
cites work: On 𝑃𝐿 de Rham theory and rational homotopy type
cites work: A classification theorem for diagrams of simplicial sets
cites work: Cech and Steenrod homotopy theories with applications to geometric topology
cites work: Systems of Fixed Point Sets
cites work: On the Equivariant Formality of Kähler Manifolds With Finite Group Action
cites work: The rational homotopy theory of certain path spaces with applications to geodesics
cites work: Lectures on minimal models
cites work: Modele Minimal Equivariant et Formalite
cites work: Transformation groups and algebraic \(K\)-theory
cites work: Homotopical algebra
cites work: Infinitesimal computations in topology
cites work: Equivariant Minimal Models
cites work: Q3678311
full work available at URL: s0022-4049(97)00127-8
OpenAlex ID: W2092994986
description: scientific article; zbMATH DE number 1308282