正规子群的临界指数、群扩张迁移算子的谱和Kazhdan距离
Critical exponents of normal subgroups, the spectrum of group extended transfer operators, and Kazhdan distance
摘要：
对于一个紧挤Hadamard流形$X$和$X$的离散等距群$Γ$，临界指数$δ_Γ$是$X$中一点在$Γ$作用下轨道的指数增长性率.证明了$Γ_0$的正规子群的$\mathcal{N}$族的临界指数与其右正则表示$Γ_0/Γ$的Kazhdan距离具有相同的粗行为.关键的工具是分析与有限型子移位相关的转移算子的谱，我们得到了一个独立有趣的结果。
英文摘要：
For a pinched Hadamard manifold $X$ and a discrete group of isometries $Γ$ of $X$, the critical exponent $δ_Γ$ is the exponential growth rate of the orbit of a point in $X$ under the action of $Γ$. We show that the critical exponent for any family $\mathcal{N}$ of normal subgroups of $Γ_0$ has the same coarse behaviour as the Kazhdan distances for the right regular representations of the quotients $Γ_0/Γ$. The key tool is to analyse the spectrum of transfer operators associated to subshifts of finite type, for which we obtain a result of independent interest.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
