## Homology, Homotopy and Applications

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

### Realization theorems for end obstructions

#### 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

**Subjects**

Primary: 57Q10: Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28] 57Q20: Cobordism 57Q40: Regular neighborhoods 57N40: Neighborhoods of submanifolds 57N80: Stratifications

**Keywords**

Stratified spaces homology homotopy

#### Citation

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