论文标题
$ l^1 $的子空间上的双曲线和统一的Lipschitz仿射动作
Hyperbolicity and uniformly Lipschitz affine actions on subspaces of $L^1$
论文作者
论文摘要
我们表明，每个双曲线组都在$ l^1 $空间的子空间上具有适当的Lipschitz仿射动作。我们还证明，每个酰基双曲线群在具有无限轨道的这样一个空间上具有均匀的Lipschitz仿射作用。我们的主要工具是由Mineyev构建的双曲线组上的$ \ Mathbb {Q} $ - 在Balasubramanya对准Trees的动作方面对酰基内向的双曲线的表征。
We show that every hyperbolic group has a proper uniformly Lipschitz affine action on a subspace of an $L^1$ space. We also prove that every acylindrically hyperbolic group has a uniformly Lipschitz affine action on such a space with unbounded orbits. Our main tools are the $\mathbb{Q}$-bicombings on hyperbolic groups constructed by Mineyev and the characterisation of acylindrical hyperbolicity in terms of actions on quasi-trees by Balasubramanya.
