交叉接线点灯组
Cross-wired lamplighter groups
摘要：
给出了Diestel-Leader图的等距群中的局部紧群同构于闭余紧子群的一个充要条件.由于这个条件，我们看到，每一个共紧格的等距群的迪斯特-领袖图承认一个传递，适当的行动，其他一些迪斯特-领袖图。我们也给出了一些实际上不是点灯人的格的例子。这意味着类的离散群可dumblighter集团是不封闭的拟等距下，并结合工作的Eskin，Fisher和Whyte，给出了一个特征的拟等距类。
英文摘要：
We give a necessary and sufficient condition for a locally compact group to be isomorphic to a closed cocompact subgroup in the isometry group of a Diestel-Leader graph. As a consequence of this condition, we see that every cocompact lattice in the isometry group of a Diestel-Leader graph admits a transitive, proper action on some other Diestel-Leader graph. We also give some examples of lattices that are not virtually lamplighters. This implies the class of discrete groups commensurable to lamplighter groups is not closed under quasi-isometries and, combined with work of Eskin, Fisher and Whyte, gives a characterization of their quasi-isometry class.
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