On the loop space of a geometric realization
type: Item
instance of: scholarly article
title: On the loop space of a geometric realization
zbMATH Open document ID: 0628.55004
DOI: 10.1016/0166-8641(87)90082-4
author: Hubertus Meiwes
published in: Topology and its Applications
publication date: 1987-01-01T00:00:00Z
review text: The author shows that if X is a good \(\Delta\)-space then there is a genuine homotopy equivalence between the model \(| \Omega X|\) constructed by \textit{H. J. Baues} [Mem. Am. Math. Soc. 230 (1980; Zbl 0473.55009)] and the loop space \(\Omega| X|\) of the geometric realization of the simplicial space \(| X|\). The realization \(\| \|\), which only refers to injective monotone maps, plays a central role in the proof. The techniques used are cofibrations, fibrations and homotopy cartesian squares. A result of Adams concerning the homology of loop spaces for simply connected spaces is obtained.
Mathematics Subject Classification ID: 55P35
Mathematics Subject Classification ID: 55U10
Mathematics Subject Classification ID: 55P10
Mathematics Subject Classification ID: 55P05
zbMATH DE Number: 4022152
zbMATH Keywords: loop space of the geometric realization of a simplicial space
zbMATH Keywords: cofibrations
zbMATH Keywords: homotopy cartesian squares
zbMATH Keywords: homology of loop spaces
reviewed by: Werner End
MaRDI profile type: Publication
full work available at URL: 0166-8641(87)90082-4
OpenAlex ID: W2016115904
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description: scientific article; zbMATH DE number 4022152