Inducing Maps Between Gromov Boundaries
Inducing Maps Between Gromov Boundaries
复制标题
归纳格罗莫夫边界之间的地图
DOI：
10.1007/s00009-015-0650-z
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发表时间：
2015
影响因子：
1.1
通讯作者：
Žiga Virk
中科院分区：
文献类型：
--
作者：
J. Dydak;Žiga Virk
众所周知，Gromov双曲空间的拟等距嵌入诱导其Gromov边界的拓扑嵌入。一个更一般的问题是检测类函数之间的Gromov双曲空间，诱导连续映射之间的Gromov边界。在本文中，我们引入了一类在Gromov边界之间诱导连续映射的视函数。它的子类，径向函数类，在Gromov边界之间导出Hölder映射。相反，在视觉双曲空间的Gromov边界之间的每个Hölder映射诱导出一个径向函数。我们研究了的大尺度性质与的小尺度性质之间的关系，特别是与维数理论有关的性质。特别地，我们证明了一种形式的维数提升定理。我们给出了一个自然的例子，径向维数提高地图，我们也给出了一般类的径向函数，提高渐近维数。
It is well known that quasi-isometric embeddings of Gromov hyperbolic spaces induce topological embeddings of their Gromov boundaries. A more general question is to detect classes of functions between Gromov hyperbolic spaces that induce continuous maps between their Gromov boundaries. In this paper, we introduce the class of visual functionsfthat do induce continuous mapsbetween Gromov boundaries. Its subclass, the class of radial functions, induces Hölder maps between Gromov boundaries. Conversely, every Hölder map between Gromov boundaries of visual hyperbolic spaces induces a radial function. We study the relationship between large-scale properties offand small-scale properties of, especially related to the dimension theory. In particular, we prove a form of the dimension raising theorem. We give a natural example of a radial dimension raising map and we also give a general class of radial functions that raise asymptotic dimension.