We will extend the topological Gromov-Hausdorff stability [2] from homeomorphisms to finitely generated actions. We prove that if an action is expansive and has the shadowing property, then it is topologically GH-stable. From this we derive examples of topologically GH-stable actions of the discrete Heisenberg group on tori. Finally, we prove that the topological GH-stability is an invariant under isometric conjugacy.

中文翻译：

---

Gromov-Hausdorff群体动作的稳定性

我们将扩展Gromov-Hausdorff拓扑的稳定性[2从同胚到有限生成的动作。我们证明，如果一个动作是可扩展的并且具有阴影属性，那么它在拓扑上是GH稳定的。从中我们得出了离散的Heisenberg群在圆环上的拓扑GH稳定作用的例子。最后，我们证明了等距共轭下的拓扑GH稳定性是不变的。