Decompositions of certain loop spaces.
type: Item
instance of: scholarly article
title: Decompositions of certain loop spaces.
zbMATH Open document ID: 1034.55002
DOI: 10.1016/S0022-4049(03)00106-3
author: Manfred Stelzer
published in: Journal of Pure and Applied Algebra
publication date: 2003-11-19T00:00:00Z
review text: The author studies the decomposition of loop spaces of: (1) mapping cones of maps between wedge products of Moore spaces; and (2) spaces he calls \(\mathbb{Z}/p\)-conformal which were defined by \textit{J. A. Neisendorfer} and \textit{T. Miller} [Illinois J. Math. 22, 565-579 (1978; Zbl 0396.55011)]. For the mapping cone \(C_f\) where \(f\) is a map between finite wedge products of Moore spaces of type \(p^n\), the loop space \(\Omega C_f\) has the homotopy type of a weak product space of Cohn-Moore-Neisendorfer factors under some dimensionality hypotheses and a condition on the homology of \(\Omega C_f\). For certain coformal CW complexes, the loop space is homotopy equivalent to the weak product of factor spaces of the CMF type or of \(p\)-local spheres and their loop spaces. A corollary of these results states that the Moore exponent conjecture is true for the classes of spaces for which the above results are true.
Mathematics Subject Classification ID: 55P35
Mathematics Subject Classification ID: 55Q52
Mathematics Subject Classification ID: 55P60
Mathematics Subject Classification ID: 55P62
zbMATH DE Number: 2005933
zbMATH Keywords: Moore exponent conjecture
zbMATH Keywords: Moore spaces
zbMATH Keywords: mapping cone
reviewed by: Daniel H. Gottlieb
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2005933