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Chinese Annals of Mathematics, Series B

, Volume 40, Issue 2, pp 199–212 | Cite as

Strong Embeddability for Groups Acting on Metric Spaces

  • Jun XiaEmail author
  • Xianjin Wang
Article
  • 4 Downloads

Abstract

The strong embeddability is a notion of metric geometry, which is an intermediate property lying between coarse embeddability and property A. In this paper, the permanence properties of strong embeddability for groups acting on metric spaces are studied. The authors show that a finitely generated group acting on a finitely asymptotic dimension metric space by isometries whose K-stabilizers are strongly embeddable is strongly embeddable. Moreover, they prove that the fundamental group of a graph of groups with strongly embeddable vertex groups is also strongly embeddable.

Keywords

Strong embeddability Groups action Graph of groups Relative hyperbolic groups 

2010 MR Subject Classification

20H15 20E06 20F65 

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Notes

Acknowledgement

The authors are indebted to referees for their useful comments.

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Copyright information

© Fudan University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Mathematics and StatisticsChongqing UniversityChongqingChina

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