Collapsibility of CAT(0) spaces
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- 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
triangulations.
(3) All contractible d-manifolds (d = 4) admit collapsible CAT(0) triangulations. This
discretizes a classical result by Ancel–Guilbault.
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
triangulations.
(3) All contractible d-manifolds (d = 4) admit collapsible CAT(0) triangulations. This
discretizes a classical result by Ancel–Guilbault.
Originalsprog | Engelsk |
---|---|
Tidsskrift | Geometriae Dedicata |
Vol/bind | 206 |
Udgave nummer | 1 |
Sider (fra-til) | 181-199 |
ISSN | 0046-5755 |
DOI | |
Status | Udgivet - jun. 2020 |
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