The homotopy classification of \((n-1)\)-connected \((n+4)\)-dimensional polyhedra with torsion free homology, \(n\geq 5\)
type: Item
instance of: scholarly article
title: The homotopy classification of \((n-1)\)-connected \((n+4)\)-dimensional polyhedra with torsion free homology, \(n\geq 5\)
zbMATH Open document ID: 0942.55010
published in: Expositiones Mathematicae
publication date: 2000-08-17T00:00:00Z
review text: The authors study the classification problem of the homotopy types of \((n-1)\)-connected \((n+k)\)-dimensional polyhedra \(X\) with torsion free homology. When \(n\geq k+1\), it follows from the Freudenthal suspension theorem that this classification problem depends only on \(k\) and not on \(n\) and they study this problem in this situation. Since the classification is solved for \(k\leq 3\), they consider the case \(k=4\) in this paper. They obtain the complete classification of homotopy types for the case \(k=4\). In particular, they give the complete list \(X(\mathcal L)\) consisting of exactly 67 polyhedra such that, if \(X\) is an \((n-1)\)-connected \((n+4)\)-dimensional polyhedron \(X\) with torsion free homology \((n\geq 5)\), then there is a homotopy equivalence \(X\simeq \bigvee_{j=1}^k X_j\) with each \(X_j\in X(\mathcal L)\).
Mathematics Subject Classification ID: 55P15
Mathematics Subject Classification ID: 52B99
Mathematics Subject Classification ID: 55P10
Mathematics Subject Classification ID: 55P40
zbMATH DE Number: 1310245
zbMATH Keywords: homotopy type
zbMATH Keywords: polyhedra
zbMATH Keywords: CW-complex
author: Hans-Joachim Baues
author: Yu. Drozd
reviewed by: Kohhei Yamaguchi
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1310245