论文标题
简单络合物和幼崽空间的链接条件
A link condition for simplicial complexes, and CUB spaces
论文作者
论文摘要
我们通过独特的凸形测量双栓来激励对度量空间的研究，我们称之为幼崽空间。这些涵盖了许多非阳性曲率的经典概念，例如CAT（0）空间和Busemann-Convex空间。在幼崽空间上有几何作用的小组享有许多特性。 我们想知道何时具有天然多面体度量的简单复合物是幼崽。我们建立了一个链路条件，从本质上说该复合物在局部是晶格。这概括了Gromov的Cube Complexs的链接条件，用于$ \ ell^\ infty $ metric。 链接条件适用于许多例子，包括欧几里得建筑物，群体的简单，欧几里得artin组的Artin络合物，（弱）Garside组，一些弧形和曲线复合物以及结的最小跨度表面。
We motivate the study of metric spaces with a unique convex geodesic bicombing, which we call CUB spaces. These encompass many classical notions of nonpositive curvature, such as CAT(0) spaces and Busemann-convex spaces. Groups having a geometric action on a CUB space enjoy numerous properties. We want to know when a simplicial complex, endowed with a natural polyhedral metric, is CUB. We establish a link condition, stating essentially that the complex is locally a lattice. This generalizes Gromov's link condition for cube complexes, for the $\ell^\infty$ metric. The link condition applies to numerous examples, including Euclidean buildings, simplices of groups, Artin complexes of Euclidean Artin groups, (weak) Garside groups, some arcs and curve complexes, and minimal spanning surfaces of knots.
