In the mathematical subject of geometric group theory, an acylindrically hyperbolic group is a group admitting a non-elementary 'acylindrical' isometric action on some geodesic hyperbolic metric space.[1] This notion generalizes the notions of a hyperbolic group and of a relatively hyperbolic group and includes a significantly wider class of examples, such as mapping class groups and Out(Fn).
^Osin, D. (2016). "Acylindrically hyperbolic groups". Transactions of the American Mathematical Society. 368 (2): 851–888. arXiv:1304.1246. doi:10.1090/tran/6343. MR 3430352. S2CID 21624534.
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geometric group theory, an acylindricallyhyperbolicgroup is a group admitting a non-elementary 'acylindrical' isometric action on some geodesic hyperbolic metric...
A group is said to be acylindricallyhyperbolic if it admits a non-elementary acylindrical action on a (not necessarily proper) Gromov-hyperbolic space...
p. 436, ISBN 9780821839461. Kapovich, Michael (2009), Hyperbolic Manifolds and Discrete Groups, Progress in Mathematics, vol. 183, Springer, p. 6, ISBN 9780817649135...
pp. ISBN 0-691-08304-5 William Thurston, Hyperbolic structures on 3-manifolds. I. Deformation of acylindrical manifolds. Ann. of Math. (2) 124 (1986),...
one can show that for a finitely presented word-hyperbolicgroup G {\displaystyle G} the hyperbolic boundary of G {\displaystyle G} has topological dimension...
for the solution of the isomorphism problem for torsion-free word-hyperbolicgroups and for the solution of the Tarski conjecture about equivalence of...
a word-hyperbolicgroup on its boundary. Bowditch also proved that (modulo a few exceptions) the boundary of a one-ended word-hyperbolicgroup G has local...
conjecture. Thurston, William P. (1986), "Hyperbolic structures on 3-manifolds. I. Deformation of acylindrical manifolds", Annals of Mathematics, Second...
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