Collapsibility of CAT(0) spaces

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Collapsibility is a combinatorial strengthening of contractibility. We relate this property to
metric geometry by proving the collapsibility of any complex that is CAT(0) with a metric
for which all vertex stars are convex. This strengthens and generalizes a result by Crowley.
Further consequences of our work are:
(1) All CAT(0) cube complexes are collapsible.
(2) Any triangulated manifold admits a CAT(0) metric if and only if it admits collapsible
(3) All contractible d-manifolds (d = 4) admit collapsible CAT(0) triangulations. This
discretizes a classical result by Ancel–Guilbault.
TidsskriftGeometriae Dedicata
Udgave nummer1
Sider (fra-til)181-199
StatusUdgivet - jun. 2020

ID: 243311187