Strong embeddability and extensions of groups

Strong embeddability and extensions of groups
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发表时间：
2013-07
期刊：
arXiv: Metric Geometry
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通讯作者：
Ronghui Ji;C. Ogle;B. Ramsey
Ronghui Ji;C. Ogle;B. Ramsey
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作者：
Ronghui Ji;C. Ogle;B. Ramsey

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We introduce the notion of strong embeddability for a metric space. This property lies between coarse embeddability and property A. A relative version of strong embeddability is developed in terms of a family of set maps on the metric space. When restricted to discrete groups, this yields relative coarse embeddability. We verify that groups acting on a metric space which is strongly embeddable has this relative strong embeddability, provided the stabilizer subgroups do. As a corollary, strong embeddability is preserved under group extensions.