发表机构
University of Copenhagen（哥本哈根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
证明了有限生成群G在紧黎曼流形M上的自由等距作用对应的离散化扭曲锥不具有几何性质(T)
AI 中文摘要
假设G是有限生成群，M是紧黎曼流形，G在M上的作用是自由等距作用，我们证明对应的离散化扭曲锥不具有几何性质(T)
英文摘要
Suppose that $G$ is a finitely generated group, $M$ is a compact Riemannian manifold and $G\curvearrowright M$ is a free and isometric action. We prove that the associated discretized warped cone does not have geometric property (T). In contrast, we show that the discretized warped cone associated to the natural action $SL_m(\mathbb Z)\curvearrowright \mathbb T^m$ has geometric property (T) for $m\geq 3$. We also prove that, for free probability-measure-preserving Lipschitz actions on compact Riemannian manifolds, geometric property (T) of the discretized warped cone implies Kazhdan's property (T) of the acting group.
CommentsAn example of action whose warped cone has geometric property (T) was added
