Collapsibility of CAT(0) spaces
Collapsibility of CAT(0) spaces
复制标题
DOI：
10.1007/s10711-019-00481-x
复制
发表时间：
2011-07
影响因子：
0.5
通讯作者：
Karim A. Adiprasito;Bruno Benedetti
中科院分区：
文献类型：
--
作者：
Karim A. Adiprasito;Bruno Benedetti
可压缩性是可收缩性的组合加强。我们将此属性度量几何证明的可扩展性的任何复杂的iswith度量的所有顶点星是凸的。这加强和推广了Crowley的一个结果。进一步的结果是：（1）全立方体复合体是可塌缩的.（2）任何三角剖分流形容许度量的当且仅当它容许可塌缩三角剖分。（3）所有可收缩流形（）都允许可压缩三角剖分。这使得安塞尔-吉尔博的经典结果变得不可信。
Collapsibility is a combinatorial strengthening of contractibility. We relate this property to metric geometry by proving the collapsibility of any complex that iswith a metric for which all vertex stars are convex. This strengthens and generalizes a result by Crowley. Further consequences of our work are:(1)Allcube complexes are collapsible.(2)Any triangulated manifold admits ametric if and only if it admits collapsible triangulations.(3)All contractibled-manifolds () admit collapsibletriangulations. This discretizes a classical result by Ancel–Guilbault.