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| Strong Embeddability for Groups Acting on Metric Spaces |
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Citation： |
Jun XIA,Xianjin WANG.Strong Embeddability for Groups Acting on Metric Spaces[J].Chinese Annals of Mathematics B,2019,40(2):199~212 |
| Page view： 2273
Net amount： 1705 |
Authors： |
Jun XIA; Xianjin WANG |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11231002, 11771061). |
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| 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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