Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Acylindrically hyperbolic groups

Author: D. Osin
Journal: Trans. Amer. Math. Soc. 368 (2016), 851-888
MSC (2010): Primary 20F67, 20F65
Published electronically: May 22, 2015
MathSciNet review: 3430352
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 20F67, 20F65

Retrieve articles in all journals with MSC (2010): 20F67, 20F65

Additional Information

D. Osin
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240

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
Article copyright: © Copyright 2015 American Mathematical Society

American Mathematical Society