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Gromov-Hausdorff stability for group actions

KL and MD were supported by the NRF grant funded by the Korea government (MSIT)(NRF-2018R1A2B3001457). CAM was partially supported by the NRF Brain Pool Grant funded by the Korea government and CNPq from Brazil

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  • 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.

    Mathematics Subject Classification: Primary: 37B25; Secondary: 53C23.


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