Strong Embeddability for Groups Acting on Metric Spaces

Citation:

Jun XIA,Xianjin WANG.Strong Embeddability for Groups Acting on Metric Spaces[J].Chinese Annals of Mathematics B,2019,40(2):199~212
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Authors:

Jun XIA; Xianjin WANG

Foundation:

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

Classification:

20H15, 20E06, 20F65
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