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- W2963176827 abstract "We say that a group <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=application/x-tex>G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is <italic>acylindrically hyperbolic</italic> 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 <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C Subscript g e o m> <mml:semantics> <mml:msub> <mml:mi>C</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>g</mml:mi> <mml:mi>e</mml:mi> <mml:mi>o</mml:mi> <mml:mi>m</mml:mi> </mml:mrow> </mml:msub> <mml:annotation encoding=application/x-tex>C_{geom}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> 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." @default.
- W2963176827 created "2019-07-30" @default.
- W2963176827 creator A5016824113 @default.
- W2963176827 date "2015-05-22" @default.
- W2963176827 modified "2023-10-04" @default.
- W2963176827 title "Acylindrically hyperbolic groups" @default.
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- W2963176827 doi "https://doi.org/10.1090/tran/6343" @default.
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