Remarks on strong embeddability for discrete metric spaces and groups

Guoqiang Li; Xianjin Wang

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Remarks on strong embeddability for discrete metric spaces and groups

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arxiv 1709.02522 v1 pith:O7UIQAP5 submitted 2017-09-08 math.FA math.MG

Guoqiang Li , Xianjin Wang This is my paper

classification math.FAmath.MG

keywords metricembeddabilityembeddablespacestrongstronglyasymptoticcoarse

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abstract

In this paper, we show that the strong embeddability has fibering permanence property and is preserved under the direct limit for the metric space. Moreover, we show the following result: let $G$ is a finitely generated group with a coarse quasi-action on a metric space $X$. If $X$ has finite asymptotic dimension and the quasi-stabilizers are strongly embeddable, then $G$ is also strongly embeddable.

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