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2008 Realization theorems for end obstructions
Bogdan Vajiac
Homology Homotopy Appl. 10(2): 1-12 (2008).


A stratified space is a filtered space with manifolds as its strata. Connolly and Vajiac proved an end theorem for stratified spaces, generalizing earlier results of Siebenmann and Quinn. Their main result states that there is a single $K$-theoretical obstruction to completing a tame-ended stratified space. A necessary condition to completeness is to find an exhaustion of the stratified space, i.e. an increasing sequence of stratified spaces with bicollared boundaries, whose union is the original space. In this paper we give an example of a stratified space that is not exhaustible. We also prove that the Connolly-Vajiac end obstructions can be realized.


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Bogdan Vajiac. "Realization theorems for end obstructions." Homology Homotopy Appl. 10 (2) 1 - 12, 2008.


Published: 2008
First available in Project Euclid: 1 September 2009

zbMATH: 1160.57019
MathSciNet: MR2426127

Primary: 57N40 , 57N80 , 57Q10 , 57Q20 , 57Q40

Keywords: homology , homotopy , stratified spaces

Rights: Copyright © 2008 International Press of Boston


Vol.10 • No. 2 • 2008
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