AI 中文总结
研究分层双曲群双曲正规子群的 Cannon - Thurston 映射不存在性，涵盖曲面映射类群正规子群等，还证明了自由循环群子群相关结果及 CAT(0)群可视边界与相对分层双曲边界同胚。
AI 中文摘要
我们证明了对于分层双曲群的双曲正规子群，无论是在莫尔斯边界还是分层双曲边界上，Cannon - Thurston 映射都不存在。该结果涵盖了亏格\(g\geq 2\)的曲面映射类群的一大类正规子群。作为推论，我们还证明了大多数自由循环群的子群的不存在性结果。此外，我们证明了具有孤立平坦的 CAT(0)群的可视边界与其作用空间的相对分层双曲边界同胚，从而恢复了先前已知的具有孤立平坦的 CAT(0)群的不存在性结果。
英文摘要
We prove that Cannon--Thurston maps do not exist for hyperbolic normal subgroups of hierarchically hyperbolic groups, both for Morse and hierarchically hyperbolic boundaries. This result includes a large class of normal subgroups of the mapping class group of a surface of genus $g\geq 2$. As a corollary, we also prove a non-existence result for subgroups of most free by cyclic groups. Moreover, we prove that the visual boundary of a CAT(0) group with isolated flats is homeomorphic to the relatively hierarchically hyperbolic boundary of the space it acts on, thus recovering a previously known non-existence result for CAT(0) groups with isolated flats.
Comments18 pages. Comments are welcome!
