Strong Embeddability for Groups Acting on Metric Spaces

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.

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Acknowledgement

The authors are indebted to referees for their useful comments.

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Correspondence to Jun Xia.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11231002, 11771061).

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Xia, J., Wang, X. Strong Embeddability for Groups Acting on Metric Spaces. Chin. Ann. Math. Ser. B 40, 199–212 (2019). https://doi.org/10.1007/s11401-019-0126-8

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Keywords

  • Strong embeddability
  • Groups action
  • Graph of groups
  • Relative hyperbolic groups

2010 MR Subject Classification

  • 20H15
  • 20E06
  • 20F65