The asymptotic dimension of a curve graph is finite
The asymptotic dimension of a curve graph is finite
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DOI：
10.1112/jlms/jdm090
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发表时间：
2005-09
期刊：
影响因子：
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通讯作者：
G. Bell;K. Fujiwara
中科院分区：
文献类型：
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作者：
G. Bell;K. Fujiwara
我们找到了一个上界的渐近维数的双曲度量空间与一组测地线满足一定的有界性条件的Bowditch研究。主要的例子是一个紧凑的可定向曲面的曲线图上的紧密测地线的集合。我们利用这一点得出结论，曲线图有一个有限的渐近维数。由此可见，曲线图具有属性A1。我们还计算了亏格至多为2的可定向曲面的映射类群的渐近维数。
We find an upper bound for the asymptotic dimension of a hyperbolic metric space with a set of geodesics satisfying a certain boundedness condition studied by Bowditch. The primary example is a collection of tight geodesics on the curve graph of a compact orientable surface. We use this to conclude that a curve graph has a finite asymptotic dimension. It follows then that a curve graph has property A1. We also compute the asymptotic dimension of mapping class groups of orientable surfaces with genus at most 2.