井位移表示和轨道图
Well displacing representations and orbit maps
摘要：
本文讨论了群的等距群作用的一个性质，即“井置换”。如果一个动作的位移函数等价于它在凯莱图上的位移函数，则称该动作是良位移的。我们与这个属性的事实，轨道映射是准等距嵌入。我们首先描述的例子表明，这两个概念是无关的一般。另一方面，我们解释说，对于某一类群-特别是双曲群-这两个属性是等价的。在我们的讨论过程中，我们引入了群的一个固有性质--我们称之为U-性质--它定量地说明了一个元素的范数如何被许多相关共轭类的平移长度所控制。这个属性在我们的讨论中起着中心作用。
英文摘要：
We discuss in this article a property of action of groups by isometries called "well displacing". An action is said to be well displacing, if the displacement function is equivalent to the the displacement function for the action on the Cayley graph. We relate this property with the fact that orbit maps are quasi-isometric embeddings. We first describe countrexamples that shows this two notions are unrelated in general. On the other hand we explain that for a certain class of groups -- in particular hyperbolic groups -- these two properties are equivalent. In the course of our discussion, we introduce an intrinsic property of the group -- that we called the U-property -- which says quantitatively how the norm an element is controlled by the translation length of finitely many related conjugacy classes. This property play a central role in our discussion.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
