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 …

We provide new examples of acylindrically hyperbolic groups arising from actions on
simplicial trees. In particular, we consider amalgamated products and HNN-extensions, one …

For every group G, we define the set of hyperbolic structures on G, denoted by ℋ (G), which
consists of equivalence classes of (possibly infinite) generating sets of G such that the …

The goal of this article is to survey some recent developments in the study of groups acting
on hyperbolic spaces. We focus on the class of acylindrically hyperbolic groups; it is broad …

We prove that finite-index subgroups of right-angled Artin groups are conjugacy separable.
We then apply this result to establish various properties of other classes of groups. In …

We prove that the outer automorphism group Out. G/is residually nite when the group G is
virtually compact special (in the sense of Haglund and Wise) or when G is isomorphic to the …

We prove that the automorphism group of every infinitely ended finitely generated group is
acylindrically hyperbolic. In particular Aut (F n) is acylindrically hyperbolic for every n⩾ 2 …

A theorem of Farb and Handel [Publ. Math. Inst. Hautes Études Sci. 105 (2007), pp. 1–48]
asserts that for $ N\ge 4$, the natural inclusion from $\mathrm {Out}(F_N) $ into its abstract …

We study subgroups and quotients of outer automorphsim groups of right-angled Artin
groups (RAAGs). We prove that for all RAAGs, the outer automorphism group is residually …

The outer automorphism group Out (G) of a group G acts on the set of conjugacy classes of
elements of G. McCool proved that the stabilizer Mc (C) of a finite set of conjugacy classes is …