The asymptotic dimension of a curve graph is finite

Bell GC; Fujiwara K

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The asymptotic dimension of a curve graph is finite

机译：曲线图的渐近维数是有限的

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摘要

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 A,. We also compute the asymptotic dimension of mapping class groups of orientable surfaces with genus at most 2.

机译：我们找到了一个双曲线度量空间的渐近维数的上界，该空间具有满足Bowditch研究的一定有界条件的一组测地线。主要示例是紧密可定向曲面的曲线图上的紧密测地线集合。我们以此得出结论，曲线图具有有限的渐近维数。因此，曲线图具有属性A ，。我们还计算类属最多为2的可定向曲面的映射类组的渐近维。

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来源
《The Journal of the London Mathematical Society》 |2008年第1期|共18页
作者
Bell GC; Fujiwara K;
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正文语种 eng
中图分类数学;
关键词
NOVIKOV-CONJECTURE; HYPERBOLIC GROUPS; METRIC-SPACES; PROPERTY-A; GEOMETRY;

机译：诺维科夫猜想;双曲群;度量空间;A属性;几何;

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机译：曲线图的渐近维是有限的

The asymptotic dimension of a curve graph is finite

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