Gromov-Hausdorff stability for group actions

Meihua Dong; Keonhee Lee; Carlos Morales

doi:10.3934/dcds.2020320

Article Contents

2021, Volume 41, Issue 3: 1347-1357. Doi: 10.3934/dcds.2020320

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Gromov-Hausdorff stability for group actions

1.
Department of Mathematics, College of Science, Yanbian University, No. 977, Gongyuan Road, Yanji City 133002, Jilin Province, China
2.
Department of Mathematics, Chungnam National University, Daejeon 305-764, Korea
3.
Instituto de Matemática, Universidade Federal do Rio de Janeiro, P. O. Box 68530 21945-970, Rio de Janeiro, Brazil

Received: January 31, 2020

Revised: June 30, 2020

Early access: August 2020

Published: March 2021

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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Abstract

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.

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

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References

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