2015/12/20 by Karim A. Adiprasito, Adiprasito, Karim A., Louis Funar +1
Mathematics · #51K10 #57N15 #57N16 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:51K10 #msc:57N15 #msc:57N16
paper · pdf · doi:10.48550/arxiv.1512.06403
26p., 6 figures
arxiv created 2021/12/26 · arxiv updated 2021/12/28
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 τ∞(M). Moreover, this implies that M is topologically collapsible, when n≥ 6. Conversely, any finite dimensional collapsible polyhedron is PL homeomorphic to a CAT(0) cubical complex.