Collapsibility of CAT(0) spaces

Karim Adiprasito; Bruno Benedetti

doi:10.1007/s10711-019-00481-x

Collapsibility of CAT(0) spaces

Karim Adiprasito, Bruno Benedetti^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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 language	English
Pages (from-to)	181-199
Number of pages	19
Journal	Geometriae Dedicata
Volume	206
Issue number	1
DOIs	https://doi.org/10.1007/s10711-019-00481-x
State	Published - 1 Jun 2020

Bibliographical note

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

Keywords

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

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Collapsibility of CAT(0) spaces

Abstract

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Keywords

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