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arXiv · 1107.5789

Collapsibility of CAT(0) spaces

Karim Adiprasito·Bruno Benedetti
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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 ($d \ne 4$) admit collapsible CAT(0) triangulations. This discretizes a classical result by Ancel--Guilbault.

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Karim Adiprasito, Bruno Benedetti. 2011-07-28. Collapsibility of CAT(0) spaces. https://arxiv.org/abs/1107.5789

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