Homology, Homotopy and Applications

Volume 10 (2008)

Number 2

Realization theorems for end obstructions

Pages: 1 – 12

DOI: https://dx.doi.org/10.4310/HHA.2008.v10.n2.a1


Bogdan Vajiac (Department of Mathematics, Saint Mary’s College, Notre Dame, Indiana, U.S.A.)


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.


stratified spaces, homology, homotopy

2010 Mathematics Subject Classification

57N40, 57N80, 57Q10, 57Q20, 57Q40

Published 1 January 2008