Collapsibility of CAT(0) spaces
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- Collapsibility of CAT(0) spaces
Accepted author manuscript, 428 KB, PDF document
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.
| Original language | English |
|---|---|
| Journal | Geometriae Dedicata |
| Volume | 206 |
| Issue number | 1 |
| Pages (from-to) | 181-199 |
| ISSN | 0046-5755 |
| DOIs | |
| Publication status | Published - Jun 2020 |
- CAT(0) spaces, Collapsibility, Discrete Morse theory, Convexity, Evasiveness, Triangulations
Research areas
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