Boundaries of acylindrically hyperbolic groups and applications

点击翻译按钮获取中文摘要

The project is devoted to the Investigation of topological and geometric properties of finitely generated groups which admit an acylindrical action on some hyperbolic space, in particular regarding their asymptotic geometry. The main distant goal is the construction of universally amenable compact boundaries as well as of affine isometric actions on L^p-spaces. Furthermore we aim at establishing rigidity properties for asymptotical invariants of fundamental groups of closed negatively curved manifolds.