A Combination Theorem for Metric Bundles
A Combination Theorem for Metric Bundles
复制标题
度量束的组合定理
DOI：
10.1007/s00039-012-0196-1
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发表时间：
2009
影响因子：
2.2
通讯作者：
Pranab Sardar
中科院分区：
文献类型：
--
作者：
Mahan Mj;Pranab Sardar
在边空间到顶点空间的包含是一致的、粗满射的拟等距的特殊情况下，我们引入了度量(图)丛的概念，它是度量空间树概念的粗几何推广。在此基础上，我们证明了拟等距截面的存在性。然后，我们证明了度量(图)丛的一个组合定理，它建立了度量(图)丛是双曲的充分条件，特别是张开的充分条件。我们用它来给出双曲圆盘上的曲面丛的例子，它的泛覆盖是Gromov-双曲的。我们还表明，在典型情况下，张开也是必要条件。
We introduce the notion of metric (graph) bundles which provide a coarse-geometric generalization of the notion of trees of metric spaces a la Bestvina–Feighn in the special case that the inclusions of the edge spaces into the vertex spaces are uniform coarsely surjective quasi-isometries. We prove the existence of quasi-isometric sections in this generality. Then we prove a combination theorem for metric (graph) bundles that establishes sufficient conditions, particularly flaring, under which the metric bundles are hyperbolic. We use this to give examples of surface bundles over hyperbolic disks, whose universal cover is Gromov-hyperbolic. We also show that in typical situations, flaring is also a necessary condition.
Teichmüller 空间中的双曲空间
影响因子：
2.6
作者：
Leininger C
通讯作者：
Leininger C