Collapsibility of CAT(0) spaces

Karim Adiprasito, Bruno Benedetti

Research output: Contribution to journalArticle

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 languageEnglish (US)
JournalGeometriae Dedicata
DOIs
StateAccepted/In press - Jan 1 2019

Fingerprint

Collapsibility
CAT(0)
CAT(0) Spaces
Triangulation
Metric Geometry
Contractibility
Metric
Strengthening
Regular hexahedron
Star
If and only if
Generalise
Vertex of a graph

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Collapsibility of CAT(0) spaces. / Adiprasito, Karim; Benedetti, Bruno.

In: Geometriae Dedicata, 01.01.2019.

Research output: Contribution to journalArticle

@article{f6dfc98db4444c79ad38b256566aba07,
title = "Collapsibility of CAT(0) spaces",
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.",
keywords = "CAT (0) spaces, Collapsibility, Convexity Evasiveness, Discrete Morse theory, Triangulations",
author = "Karim Adiprasito and Bruno Benedetti",
year = "2019",
month = "1",
day = "1",
doi = "10.1007/s10711-019-00481-x",
language = "English (US)",
journal = "Geometriae Dedicata",
issn = "0046-5755",
publisher = "Springer Netherlands",

}

TY - JOUR

T1 - Collapsibility of CAT(0) spaces

AU - Adiprasito, Karim

AU - Benedetti, Bruno

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - CAT (0) spaces

KW - Collapsibility

KW - Convexity Evasiveness

KW - Discrete Morse theory

KW - Triangulations

UR - http://www.scopus.com/inward/record.url?scp=85073981004&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85073981004&partnerID=8YFLogxK

U2 - 10.1007/s10711-019-00481-x

DO - 10.1007/s10711-019-00481-x

M3 - Article

AN - SCOPUS:85073981004

JO - Geometriae Dedicata

JF - Geometriae Dedicata

SN - 0046-5755

ER -