论文标题
公制树木的组合定理
A Combination Theorem for Trees of Metric Bundles
论文作者
论文摘要
由Bestvina-Feighn（[BF92]）和MJ-Sardar（[MS12]）的工作激励，我们定义了公制捆绑树的树木，以汇总公制空间和度量捆绑包的树木。然后，我们证明了这些空间的组合定理。更准确地说，我们证明，如果保持以下内容，则一束公制捆绑树是双曲线的（请参见定理1.4）。 $（1）$纤维是均匀的双曲度度量空间，基数也是双曲度度量空间，$（2）$（2）$ barycenter图的纤维图均匀地过滤了过滤量，$（3）$（3）$边缘空间均匀地嵌入了相应的纤维和$（4）$（4）$（4）$ bestvina-feighn flareyn's flaringny's flaighn's flaighn's flareyn's flaring's flainsy's flainsy's flainsy's flaring's flainey's flains flaring。 作为应用程序，我们为有限的简单复合物的某些组的某些组合物提供了组合定理（请参见定理1.2）。
Motivated by the work of Bestvina-Feighn ([BF92]) and Mj-Sardar ([MS12]), we define trees of metric bundles subsuming both the trees of metric spaces and the metric bundles. Then we prove a combination theorem for these spaces. More precisely, we prove that a tree of metric bundles is hyperbolic if the following hold (see Theorem 1.4). $(1)$ The fibers are uniformly hyperbolic metric spaces and the base is also hyperbolic metric space, $(2)$ barycenter maps for the fibers are uniformly coarsely surjective, $(3)$ the edge spaces are uniformly qi embedded in the corresponding fibers and $(4)$ Bestvina-Feighn's flaring condition is satisfied. As an application, we provide a combination theorem for certain complexes of groups over finite simplicial complex (see Theorem 1.2).
