  We prove that an open manifold $M$ of dimension at least $5$ which admits a
complete CAT(0) polyhedral metric is pseudo-collarable, its fundamental group
at infinity is strongly perfectly semistable and has vanishing
Chapman-Siebenmann obstruction $\tau_{\infty}(M)$. Moreover, this implies that
$M$ is topologically collapsible, when $n\geq 6$. Conversely, any finite
dimensional collapsible polyhedron is PL homeomorphic to a CAT(0) cubical
complex.
