Realization theorems for end obstructions
type: Item
instance of: scholarly article
title: Realization theorems for end obstructions
zbMATH Open document ID: 1160.57019
author: Bogdan Vajiac
published in: Homology, Homotopy and Applications
publication date: 2008-08-11T00:00:00Z
full work available at URL: n2
review text: When is an open manifold the interior of a compact manifold with boundary? Siebenmann answered this question (for high dimensional manifolds) in his thesis [\textit{L. C. Siebenmann}, Obstructions to finding a boundary for an open manifold, Ph.D. Thesis, Princeton Univ, (1965)], \textit{F. Quinn} [Ann. Math. (2) 110, 275--331 (1979; Zbl 0394.57022)] provided an important controlled version, and \textit{F. Connolly} and \textit{B. Vajiac} [Invent. Math. 135, No.~3, 519--543 (1999; Zbl 0930.57025)] obtained stratified versions. In particular, given a manifold stratified space \(X\), there is a controlled Quinn-type obstruction whose vanishing implies that \(X\) is the interior of a compact manifold stratified space. The current paper provides examples realizing the obstructions. Moreover, an interesting example is given of a manifold stratified space with a tame end that is not the increasing union of compact manifold stratified spaces with bicollared boundaries.
reviewed by: Bruce Hughes
Mathematics Subject Classification ID: 57N80
Mathematics Subject Classification ID: 57N40
Mathematics Subject Classification ID: 57Q10
Mathematics Subject Classification ID: 57Q40
Mathematics Subject Classification ID: 57S17
zbMATH DE Number: 5309451
zbMATH Keywords: stratified space
zbMATH Keywords: Siebenmann's thesis
zbMATH Keywords: end obstructions
zbMATH Keywords: controlled topology
MaRDI profile type: Publication
OpenAlex ID: W2052493580
DOI: 10.4310/HHA.2008.V10.N2.A1
description: scientific article; zbMATH DE number 5309451