Gromov-Hausdorff stability for group actions
The paper is a sequel to the work done by the first and third authors in [Discrete Contin. Dyn. Syst. 37, No. 7, 3531--3544 (2017; Zbl 1369.54024)] where a new notion of stability for homeomorphisms was introduced (Gromov-Hausdorff (GH) stability). Roughly speaking, this is a stability concept in a setting in which both the homeomorphism and the ambient space vary. Here the authors extend the notion of topological GH stability from homeomorphisms to finitely generated actions. The main result is that if an action is expansive and has the shadowing property, then it is topologically GH-stable. As a consequence they obtain examples of topologically GH-stable actions of the discrete Heisenberg group on tori. They also prove that the topological GH stability is an invariant under isometric conjugacy.
scientific article; zbMATH DE number 7314912