The Tits boundary of a CAT(0) 2-complex
The Tits boundary of a CAT(0) 2-complex
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CAT(0) 2 复形的 Tits 边界
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
Xiangdong Xie
中科院分区：
文献类型：
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作者：
Xiangdong Xie
我们研究了只有有限个等距细胞类型的CAT(0)2-络合物的Tits边界。特别地，我们证明了在远离端点的情况下，Tits边界中的测地线段是等距嵌入的欧氏扇区的理想边界。作为应用，我们给出了Tits边界上的两点是2-复形中测地线的端点以及由两条双曲等距线生成的群包含自由群的充分条件。我们还证明了如果两个CAT(0)2-复形是拟等距的，则它们的Tits边界的核是双Lipschitz的。
We investigate the Tits boundary of CAT(0) 2-complexes that have only a finite number of isometry types of cells. In particular, we show that away from the endpoints, a geodesic segment in the Tits boundary is the ideal boundary of an isometrically embedded Euclidean sector. As applications, we provide sufficient conditions for two points in the Tits boundary to be the endpoints of a geodesic in the 2-complex and for a group generated by two hyperbolic isometries to contain a free group. We also show that if two CAT(0) 2-complexes are quasi-isometric, then the cores of their Tits boundaries are bi-Lipschitz.