Collapsibility of CAT(0) spaces
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Collapsibility of CAT(0) spaces. / Adiprasito, Karim; Benedetti, Bruno.
In: Geometriae Dedicata, Vol. 206, No. 1, 06.2020, p. 181-199.Research output: Contribution to journal › Journal article › Research › peer-review
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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