无限型映射类的极限叶状结构与边界权重
Limiting laminations and boundary weights for infinite-type mapping classes
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中文总结 AI 辅助
本文研究无限型曲面上的映射类，构造了轨道分裂为 n 个子序列的映射类，其极限叶状结构被循环置换，并证明相对弧图边界上的吸引极限点权重为 n，实现了所有有限权重。
中文摘要 AI 辅助
对于每个具有孤立尖点且允许移位映射的无限型曲面，以及每个自然数 $n$，我们研究了一个本质无限型映射类 $g_n$ 和一条简单闭曲线，该曲线在 $g_n$ 作用下的轨道分裂为 $n$ 个子序列，每个子序列在粗 Chabauty 拓扑下收敛到曲面上的一个测地线叶状结构。这些叶状结构被 $g_n$ 循环置换，它们的并集是一个 $g_n$ 不变的测地线叶状结构。我们进一步证明了 $g_n$ 在相对弧图边界上的吸引极限点具有权重 $n$。特别地，相对弧图的本质无限型 loxodromic 等距实现了所有有限权重。
英文摘要
For every infinite-type surface with an isolated puncture that admits a shift map and every natural number $n$, we study an intrinsically infinite-type mapping class $g_n$ and a simple closed curve whose orbit under $g_n$ splits into $n$ subsequences, each of which converges in the coarse Chabauty topology to a geodesic lamination on the surface. These laminations are cyclically permuted by $g_n$, and their union is a $g_n$--invariant geodesic lamination. We further show the attracting limit point of $g_n$ in the boundary of the relative arc graph has weight $n$. In particular, intrinsically infinite-type loxodromic isometries of the relative arc graph realize every finite weight.
