A generalization of the triad theorem of Blakers-Massey
type: Item
instance of: scholarly article
title: A generalization of the triad theorem of Blakers-Massey
zbMATH Open document ID: 0880.55011
DOI: 10.1016/S0040-9383(96)00045-6
author: Wojciech Chachólski
published in: Topology
publication date: 1998-02-08T00:00:00Z
review text: \textit{E. Dror-Farjoun} [Cellular spaces, null spaces and homotopy localization, Lect. Notes Math. 1622 (1995; Zbl 0842.55001)] gave a far-reaching generalization of cellular theory, by going from a space \(A\) to the smallest class containing \(A\), closed under weak equivalence, homotopy push-out and wedge. If \(X\) is in this class, it is said to be greater than or equal to \(A\). The author uses this to find a common generalization to the Blakers-Massey theorem [\textit{A. L. Blakers} and \textit{W. S. Massey}, Ann. Math., II. Ser. 53, 161-205 (1951; Zbl 0042.17301)] and known results comparing the homology of a space and homotopy limits. He also extends classical results of Serre relating \(H_*(E,F)\) and \(H_*(B)\) in a range of dimensions. A word of warning is appropriate. In spite of the very general language of the introduction, a space in this paper is a simplicial set.
Mathematics Subject Classification ID: 55Q05
Mathematics Subject Classification ID: 57Q05
zbMATH DE Number: 1034162
zbMATH Keywords: cellular spaces
zbMATH Keywords: homology of pairs
zbMATH Keywords: Blakers-Massey theorem
reviewed by: Donald W. Kahn
MaRDI profile type: Publication
full work available at URL: s0040-9383(96)00045-6
OpenAlex ID: W2049927326
description: scientific article; zbMATH DE number 1034162