Collapsibility of CAT(0) spaces

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

I: Geometriae Dedicata, Bind 206, Nr. 1, 06.2020, s. 181-199.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Adiprasito, K & Benedetti, B 2020, 'Collapsibility of CAT(0) spaces', Geometriae Dedicata, bind 206, nr. 1, s. 181-199. https://doi.org/10.1007/s10711-019-00481-x

APA

Adiprasito, K., & Benedetti, B. (2020). Collapsibility of CAT(0) spaces. Geometriae Dedicata, 206(1), 181-199. https://doi.org/10.1007/s10711-019-00481-x

Vancouver

Adiprasito K, Benedetti B. Collapsibility of CAT(0) spaces. Geometriae Dedicata. 2020 jun.;206(1):181-199. https://doi.org/10.1007/s10711-019-00481-x

Author

Adiprasito, Karim ; Benedetti, Bruno. / Collapsibility of CAT(0) spaces. I: Geometriae Dedicata. 2020 ; Bind 206, Nr. 1. s. 181-199.

Bibtex

@article{6f21544950494568a8d5084643b1cc96,
title = "Collapsibility of CAT(0) spaces",
abstract = "Collapsibility is a combinatorial strengthening of contractibility. We relate this property tometric geometry by proving the collapsibility of any complex that is CAT(0) with a metricfor 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 collapsibletriangulations.(3) All contractible d-manifolds (d = 4) admit collapsible CAT(0) triangulations. Thisdiscretizes a classical result by Ancel–Guilbault.",
keywords = "CAT(0) spaces, Collapsibility, Discrete Morse theory, Convexity, Evasiveness, Triangulations",
author = "Karim Adiprasito and Bruno Benedetti",
year = "2020",
month = jun,
doi = "10.1007/s10711-019-00481-x",
language = "English",
volume = "206",
pages = "181--199",
journal = "Geometriae Dedicata",
issn = "0046-5755",
publisher = "Springer",
number = "1",

}

RIS

TY - JOUR

T1 - Collapsibility of CAT(0) spaces

AU - Adiprasito, Karim

AU - Benedetti, Bruno

PY - 2020/6

Y1 - 2020/6

N2 - Collapsibility is a combinatorial strengthening of contractibility. We relate this property tometric geometry by proving the collapsibility of any complex that is CAT(0) with a metricfor 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 collapsibletriangulations.(3) All contractible d-manifolds (d = 4) admit collapsible CAT(0) triangulations. Thisdiscretizes a classical result by Ancel–Guilbault.

AB - Collapsibility is a combinatorial strengthening of contractibility. We relate this property tometric geometry by proving the collapsibility of any complex that is CAT(0) with a metricfor 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 collapsibletriangulations.(3) All contractible d-manifolds (d = 4) admit collapsible CAT(0) triangulations. Thisdiscretizes a classical result by Ancel–Guilbault.

KW - CAT(0) spaces

KW - Collapsibility

KW - Discrete Morse theory

KW - Convexity

KW - Evasiveness

KW - Triangulations

U2 - 10.1007/s10711-019-00481-x

DO - 10.1007/s10711-019-00481-x

M3 - Journal article

VL - 206

SP - 181

EP - 199

JO - Geometriae Dedicata

JF - Geometriae Dedicata

SN - 0046-5755

IS - 1

ER -

ID: 243311187