Disjoint spine phenomena in certain contractible \(n\)-manifolds (\(n\geq 5\))
type: Item
instance of: scholarly article
title: Disjoint spine phenomena in certain contractible \(n\)-manifolds (\(n\geq 5\))
zbMATH Open document ID: 0998.57044
DOI: 10.1016/S0166-8641(01)00079-7
published in: Topology and its Applications
publication date: 2002-08-22T00:00:00Z
review text: The present paper takes into account the problem of the existence of non trivial, compact, contractible PL-manifolds having disjoint spines; recall that this problem was originally settled, in dimension four, in connection with covering properties of Mazur manifold [\textit{D. G. Wright}, Topology 31, No. 2, 281-291 (1992; Zbl 0755.57009)]. By improving techniques of [\textit{C. R. Guilbault}, Topology 34, No. 1, 99-108 (1995; Zbl 0841.57034)] (which positively solves the problem in dimension \(n \geq 9\)) and by making use of properties about vanishing relative homotopy groups and of a suitable construction on acyclic 2-complexes, the author produces contractible manifolds with disjoint spines in dimension \(n \geq 5\). \noindent Thus, the problem results to be unsolved only in the original case of dimension four. \noindent Finally, note that both in Guilbault's work and in the present work, all provided examples belong to the class of Newman Contractible Manifolds [\textit{M. H. A. Newman}, Proc. Natl. Acad. Sci. USA 34, 193-196 (1948; Zbl 0036.12801)].
reviewed by: Maria Rita Casali
Mathematics Subject Classification ID: 57N15
Mathematics Subject Classification ID: 57Q99
zbMATH DE Number: 1787501
zbMATH Keywords: pseudospine
zbMATH Keywords: disjoint spines
zbMATH Keywords: contractible manifold
zbMATH Keywords: homology sphere
author: Manuel J. III Sanders
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1787501