Realization theorems for end obstructions
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.
scientific article; zbMATH DE number 5309451