Acylindrically hyperbolic groups
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Abstract:
We say that a group $G$ is acylindrically hyperbolic if it admits a non-elementary acylindrical action on a hyperbolic space. We prove that the class of acylindrically hyperbolic groups coincides with many other classes studied in the literature, e.g., the class $C_{geom}$ introduced by Hamenstädt, the class of groups admitting a non-elementary weakly properly discontinuous action on a hyperbolic space in the sense of Bestvina and Fujiwara, and the class of groups with hyperbolically embedded subgroups studied by Dahmani, Guirardel, and the author. We also record some basic results about acylindrically hyperbolic groups for future use.References
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Additional Information
- D. Osin
- Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
- MR Author ID: 649248
- Email: denis.v.osin@vanderbilt.edu
- Received by editor(s): April 8, 2013
- Received by editor(s) in revised form: November 8, 2013, and December 4, 2013
- Published electronically: May 22, 2015
- Additional Notes: This work was supported by NSF grant DMS-1006345 and by RFBR grant 11-01-00945
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 851-888
- MSC (2010): Primary 20F67, 20F65
- DOI: https://doi.org/10.1090/tran/6343
- MathSciNet review: 3430352