We introduce and study the notions of hyperbolically embedded and very rotating families of
subgroups. The former notion can be thought of as a generalization of the peripheral …

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 …

Let k be an algebraically closed field. We show that the Cremona group of all birational
transformations of the projective plane $\mathbb {P} _ {\mathbf {k}}^ 2$ is not a simple group …

Combinatorial Algebra: Syntax and Semantics provides comprehensive account of many
areas of combinatorial algebra. It contains self-contained proofs of more than 20 …

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 …

Let G be a group, H a hyperbolically embedded subgroup of G, V a normed G–module, U an
H–invariant submodule of V. We propose a general construction which allows to extend 1 …

Given a locally constant linear cocycle over a subshift of finite type, we show that the
existence of a uniform gap between the i-th and (i+ 1)-th Lyapunov exponents for all …

Given a countable group $ G $, let ${\rm L}(G) $ denote its von Neumann algebra. For a
wide class of ICC groups with Kazhdan's property (T), we confirm a conjecture of VFR Jones …

In this paper it is proved that relative hyperbolicity is a quasi-isometry invariant. As
byproducts of the arguments, simplified definitions of relative hyperbolicity are provided. In …

The R∞ and S∞ properties for linear algebraic groups Skip to content Should you have
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