Extension of the Borsuk theorem on non-embeddability of spheres
type: Item
instance of: scholarly article
title: Extension of the Borsuk theorem on non-embeddability of spheres
zbMATH Open document ID: 1276.57021
DOI: 10.1090/S0002-9939-2012-11238-9
author: Józef Krasinkiewicz
author: Stanisław Spież
published in: Proceedings of the American Mathematical Society
publication date: 2013-09-03T00:00:00Z
full work available at URL: https://arxiv.org/abs/0906.4710
Mathematics Subject Classification ID: 57N35
Mathematics Subject Classification ID: 54C25
Mathematics Subject Classification ID: 54E45
Mathematics Subject Classification ID: 55M10
Mathematics Subject Classification ID: 57Q05
Mathematics Subject Classification ID: 57N15
zbMATH DE Number: 6204275
zbMATH Keywords: embeddings
zbMATH Keywords: locally connected continua
zbMATH Keywords: weak manifolds
zbMATH Keywords: ramified manifolds
zbMATH Keywords: product of curves
MaRDI profile type: Publication
arXiv ID: 0906.4710
cites work: Q4070025
cites work: Q4954117
cites work: Q5813687
cites work: Q4855460
cites work: Q5837247
cites work: Generalized manifolds in products of curves
cites work: Q5338735
cites work: Q5522742
cites work: Q5837858
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review text: The authors prove that the suspension \(\sum M\) of a closed \(n\)-manifold \(M\), where \(\geq 1\), does not embed in a product of \(n+1\) curves. In particular, from this result, the following property of spheres discovered by Borsuk, is deduced: the \(n\)-sphere \(\mathbb{S}^{n}\), \(n\geq 2\), does not embed in a product of \(n\) curves. Moreover, the authors generalize the first result for locally connected quasi-\(n\)-manifolds. The proofs are based on the \textit{Second Factorization Theorem} and \textit{Second Structure Theorem} which extend the corresponding results from \textit{A. Koyama, J. Krasinkiewicz} and \textit{S. Spie\(\dot{z}\)} [Trans. Am. Math. Soc. 363, No. 3, 1509--1532 (2011; Zbl 1221.54019). Finally, the authors give a proof of the Second Factorization Theorem for ramified \(3\)-manifolds and they close by asking whether the Factorization Theorem also holds for ramified \(n\)-manifolds.
description: scientific article; zbMATH DE number 6204275