## Homology, Homotopy and Applications

### Realization theorems for end obstructions

Bogdan Vajiac

#### Abstract

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.

#### Article information

Source
Homology Homotopy Appl., Volume 10, Number 2 (2008), 1-12.

Dates
First available in Project Euclid: 1 September 2009

Permanent link to this document
https://projecteuclid.org/euclid.hha/1251811064

Mathematical Reviews number (MathSciNet)
MR2426127

Zentralblatt MATH identifier
1160.57019

#### Citation

Vajiac, Bogdan. Realization theorems for end obstructions. Homology Homotopy Appl. 10 (2008), no. 2, 1--12. https://projecteuclid.org/euclid.hha/1251811064