A connected 4-dimensional polyhedron with two homotopy decompositions into prime factors
type: Item
instance of: scholarly article
title: A connected 4-dimensional polyhedron with two homotopy decompositions into prime factors
zbMATH Open document ID: 1153.55008
author: Danuta Kołodziejczyk
published in: Topology and its Applications
publication date: 2008-11-12T00:00:00Z
review text: By using the Conner-Raymond example of some \(3\) dimensional aspherical manifolds, the author proves that there exists a connected polyhedron \(P\) of dimension \(4\) such that it has two different decompositions into prime factors in the shape category or in the homotopy category. In particular, by using this result she also gives a positive answer to a question given by K. Borsuk (1972).
reviewed by: Kohhei Yamaguchi
Mathematics Subject Classification ID: 55P55
Mathematics Subject Classification ID: 55P15
zbMATH DE Number: 5365209
zbMATH Keywords: polyhedron
zbMATH Keywords: ANR
zbMATH Keywords: homotopy type
zbMATH Keywords: shape
zbMATH Keywords: Poincaré duality group
MaRDI profile type: Publication
full work available at URL: j.topol.2007.05.023
OpenAlex ID: W2091981784
cites work: Q4070025
cites work: What is the theory of shape?
cites work: Compact flat Riemannian manifolds. I
cites work: Q5683461
cites work: Shape theory. An introduction
cites work: Poincaré duality groups of dimension two. II
cites work: Homotopy Idempotents on Finite-Dimensional Complexes Split
cites work: Q4795231
cites work: Groups with isomorphic homology groups and non-cancellation in homotopy theory
cites work: On principal \(S^ 3\)-bundles over spheres
cites work: Q4143515
cites work: Coarse Alexander duality and duality groups
cites work: Q3959112
cites work: Q3663506
cites work: Non-uniqueness of homotopy factorizations into irreducible polyhedra
cites work: Q4057285
cites work: Finiteness conditions for CW-complexes. I, II.
cites work: Q5530411
DOI: 10.1016/J.TOPOL.2007.05.023
description: scientific article; zbMATH DE number 5365209