An end theorem for stratified spaces

Abstract.

We show that a manifold-stratified space X is the interior of a compact manifold-stratified space with boundary if and only if X is tame-ended and a K-theoretic obstruction γ_*(X) vanishes. The obstruction γ_*(X) is a localization of Quinn's mapping cylinder neighborhood obstruction. The main results are Theorem 1.6 and Theorem 1.7 below. In particular, this explains when a G-manifold is the interior of a compact G-manifold with boundary. One of our methods is a new transversality theorem, Theorem 1.16.