CAT(0) metrics on contractible manifolds

Abstract

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 $n\ge 6$. Conversely, any finite dimensional collapsible polyhedron is PL homeomorphic to a CAT(0) cubical complex.

arXiv comment26p., 6 figures