A classification of 3-thickenings of 2-polyhedra
type: Item
instance of: scholarly article
title: A classification of 3-thickenings of 2-polyhedra
zbMATH Open document ID: 0928.57029
DOI: 10.1016/S0166-8641(98)00036-4
author: Nikolaj B. Brodskij
author: A. B. Skopenkov
author: Dušan Repovš
published in: Topology and its Applications
publication date: 2000-01-12T00:00:00Z
review text: The main result of the present paper guarantees the classification up to a homeomorphism of three-dimensional regular neighborhoods (3-thickenings) of a given 2-polyhedron \(P\). Two corollaries are derived for a special type of 2-polyhedra, containing fake surfaces. The first corollary proves that (i) 3-thickenings of \(P\) are classified by the restrictions of their first Stiefel-Whitney classes to \(P\) and (ii) for every two homotopic embeddings of \(P\) into the interior of a 3-manifold, the regular neighborhoods of their images are homeomorphic. The second corollary states that a fake surface is orientably 3-thickenable if and only if it does not contain a union of the Möbius band with an annulus (one of the boundary circles of the annulus attached to the middle circle of the Möbius band with a map of degree 1).
reviewed by: Octavian Pastravanu
Mathematics Subject Classification ID: 57Q40
Mathematics Subject Classification ID: 57Q25
Mathematics Subject Classification ID: 57M20
Mathematics Subject Classification ID: 57Q35
zbMATH DE Number: 1317236
zbMATH Keywords: thickening
zbMATH Keywords: fake surface
MaRDI profile type: Publication
Wikidata QID: Q127489029
full work available at URL: s0166-8641(98)00036-4
OpenAlex ID: W2118451286
description: scientific article; zbMATH DE number 1317236