ﻻ يوجد ملخص باللغة العربية
We define the notion of rough Cayley graph for compactly generated locally compact groups in terms of quasi-actions. We construct such a graph for any compactly generated locally compact group using quasi-lattices and show uniqueness up to quasi-isometry. A class of examples is given by the Cayley graphs of cocompact lattices in compactly generated groups. As an application, we show that a compactly generated group has polynomial growth if and only if its rough Cayley graph has polynomial growth (same for intermediate and exponential growth). Moreover, a unimodular compactly generated group is amenable if and only if its rough Cayley graph is amenable as a metric space.
A connected, locally finite graph $Gamma$ is a Cayley--Abels graph for a totally disconnected, locally compact group $G$ if $G$ acts vertex-transitively with compact, open vertex stabilizers on $Gamma$. Define the minimal degree of $G$ as the minimal
Suppose that $X=G/K$ is the quotient of a locally compact group by a closed subgroup. If $X$ is locally contractible and connected, we prove that $X$ is a manifold. If the $G$-action is faithful, then $G$ is a Lie group.
We construct locally compact groups with no non-trivial Invariant Random Subgroups and no non-trivial Uniformly Recurrent Subgroups.
We study abstract group actions of locally compact Hausdorff groups on CAT(0) spaces. Under mild assumptions on the action we show that it is continuous or has a global fixed point. This mirrors results by Dudley and Morris-Nickolas for actions on tr
The set of equivalence classes of cobounded actions of a group on different hyperbolic metric spaces carries a natural partial order. The resulting poset thus gives rise to a notion of the best hyperbolic action of a group as the largest element of t