Graphs of Some CAT(0) Complexes
Graphs of Some CAT(0) Complexes
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DOI：
10.1006/aama.1999.0677
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发表时间：
2000-02
期刊：
影响因子：
--
通讯作者：
V. Chepoi
中科院分区：
文献类型：
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作者：
V. Chepoi
在这篇注记中，我们在Gromov的CAT(0)意义下刻画了具有非正曲率的分段欧氏单纯复形和三次复形的图(1-骨架)。每个这样的单元复合体K是单连接的，并且遵守特定的标志条件。证明了：如果所有极大胞元都是正则欧几里德立方体或以特殊方式粘合在一起的右欧几里德三角形，则其下标图G(K)要么是中值图，要么是没有两个禁止导出子图的遗传模图。我们还刻画了桥图的单纯复形，这类图的度量具有CAT(0)空间的基本性质之一。此外，我们还证明了所有这些复形的图和一些更一般的图类的图都有测地组合和双组合来验证1-或2-同伴旅行者性质。
In this note, we characterize the graphs (1-skeletons) of some piecewise Euclidean simplicial and cubical complexes having nonpositive curvature in the sense of Gromov's CAT(0) inequality. Each such cell complex K is simply connected and obeys a certain flag condition. It turns out that if, in addition, all maximal cells are either regular Euclidean cubes or right Euclidean triangles glued in a special way, then the underlying graph G(K) is either a median graph or a hereditary modular graph without two forbidden induced subgraphs. We also characterize the simplicial complexes arising from bridged graphs, a class of graphs whose metric enjoys one of the basic properties of CAT(0) spaces. Additionally, we show that the graphs of all these complexes and some more general classes of graphs have geodesic combings and bicombings verifying the 1- or 2-fellow traveler property.