Boundaries of acylindrically hyperbolic groups and applications

该项目致力于研究在某些双曲空间上允许非圆柱作用的有限生成群的拓扑和几何性质，特别是关于它们的渐近几何。主要的远期目标是在L p-空间上构造普遍服从的紧边界和仿射等距作用。此外，我们的目的是建立闭负曲流形的基本群的渐近不变量的刚性性质。

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.