Strong Embeddability for Groups Acting on Metric Spaces
- 4 Downloads
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.
KeywordsStrong embeddability Groups action Graph of groups Relative hyperbolic groups
2010 MR Subject Classification20H15 20E06 20F65
Unable to display preview. Download preview PDF.
The authors are indebted to referees for their useful comments.
- Gromov, M., Asymptotic invariants of infinite groups, Geometric Group Theory, Niblo, A. and Roller, M. (eds.), London Mathematical Society Lecture Notes, 182, Cambridge University Press, Cambridge, 1993, 1–295.Google Scholar
- Ji, R., Ogle, C. and Ramsey, B. W., Strong embeddablility and extensions of groups, arXiv: 1307.1935.Google Scholar