Collapsibility of CAT(0) spaces

Karim Adiprasito, Bruno Benedetti*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageAmerican English
Pages (from-to)181-199
Number of pages19
JournalGeometriae Dedicata
Issue number1
StatePublished - 1 Jun 2020

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature B.V.


  • CAT (0) spaces
  • Collapsibility
  • Convexity Evasiveness
  • Discrete Morse theory
  • Triangulations


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