AI 中文总结
研究非圆柱双曲群字度量中的投影现象，对斜驶WPD元素证明相关最短投影性质，借此得到增长函数上界、构造真商群，还证明了受限子群的增长 - 余增长不等式。
AI 中文摘要
我们研究有限生成非圆柱双曲群的字度量中的投影现象。对于作用在双曲空间上的斜驶WPD元素，我们证明在字度量中到相应循环子群的最短投影次线性地跟踪到其在双曲空间中轴的最短投影的拉回。作为应用，我们得到增长函数的有效上界并构造其增长率收敛到原群增长率的真商群。我们还证明了非圆柱双曲群和具有莫尔斯元素的莫尔斯局部到全局群中受限子群的增长 - 余增长不等式。
英文摘要
We study projection phenomena in word metrics of finitely generated acylindrically hyperbolic groups. For a loxodromic WPD element acting on a hyperbolic space, we prove that shortest projection in the word metric to the corresponding cyclic subgroup sublinearly tracks the pullback of shortest projection to its axis in the hyperbolic space. As applications, we obtain effective upper bounds for growth functions and construct proper quotients whose growth rates converge to that of the original group. We further prove a growth--cogrowth inequality for confined subgroups in both acylindrically hyperbolic groups and Morse local-to-global groups with Morse elements.
Comments41 pages, 4 figures
