克莱因群路径的组合与层析
Combinations and chromatography of paths of Kleinian groups
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中文总结 AI 辅助
研究\(n\)维双曲空间等距群无挠离散子群集合\(\mathcal{D}_n\)上查布蒂拓扑的连续路径，证明组合定理构造奇异路径，引入‘层析’技术证明分解定理刻画\(\mathcal{D}_3\)中凸紧群路径。
中文摘要 AI 辅助
我们研究\(n\)维双曲空间等距群的无挠离散子群集合\(\mathcal{D}_n\)上查布蒂拓扑中的连续路径。我们证明了\(\mathcal{D}_n\)中路径的组合定理，可构造离散子群的奇异路径，其上无两个子群同构。还引入‘层析’技术证明分解定理，刻画\(\mathcal{D}_3\)中凸紧群的路径。
英文摘要
We study continuous paths in the Chabauty topology on the set $\mathcal{D}_n$ of torsion free discrete subgroups of the isometry group of $n$-dimensional hyperbolic space. We prove a combination theorem for paths in $\mathcal{D}_n$, which allows us to construct an exotic path of discrete subgroups along which no two subgroups are isomorphic. We also introduce a technique we refer to as "chromatography" to prove a decomposition theorem that characterizes paths of convex cocompact groups in $\mathcal{D}_3$.
