Collapsibility of CAT(0) spaces
Research output: Contribution to journal › Journal article › Research › peer-review
Documents
- 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
Number of downloads are based on statistics from Google Scholar and www.ku.dk
No data available
ID: 243311187