映射类群的极限集
Limit sets of mapping class groups
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中文总结 AI 辅助
该研究在射影测度叶状结构空间中为映射类群子群引入两类极限点概念，将Teichmüller测地线射线分类，且证明分类可由定向叶状结构的拓扑性质确定。
中文摘要 AI 辅助
我们针对映射类群的子群，在射影测度叶状结构空间中引入了horospherical极限点和大horospherical极限点的概念，它们类似于双曲空间中的对应概念。我们将由射影测度叶状结构所定向的Teichmüller测地线射线分为锥形、horospherical、大horospherical极限点三类，并证明这些类型可由定向叶状结构的拓扑性质确定：除了极小且唯一遍历的射影测度叶状结构对应的射线既可以是锥形极限点也可以是非锥形horospherical极限点的情况外，其余情况均可通过定向叶状结构的拓扑性质判定。
英文摘要
We introduce the notions of horospherical limit point and big horospherical limit point in the projective measured foliation space for a subgroup of the mapping class group, which are analogous to these notions for hyperbolic spaces. We classify Teichmüller geodesic rays directed by projective measured foliations into conical, horospherical, big horospherical limit points, and show that these can be determined by the topological properties of the directing foliations: except for the case of minimal and uniquely ergodic projective measured foliation, whose corresponding ray can be either a conical limit point or a non-conical horospherical limit point.
