$\text{Out}(F_n)$中的子群分解，第III部分：弱吸引理论
Subgroup decomposition in $\text{Out}(F_n)$, Part III: Weak attraction theory
摘要：
这是第三个系列的四篇论文（与研究公告张贴在此arXiv），开发了一个分解理论的子群$\text{Out}(F_n)$。在给定$F_n$的外自同构和吸引-排斥层对的条件下，研究了$F_n$中的哪些直线和共轭类在向前迭代和向后迭代下分别弱吸引到该层对.对于共轭类，我们证明了研究公告中的定理F，它给出了一个称为“非吸引子群系统”的唯一顶点群系统，它所携带的共轭类在向前迭代时被刻画为不弱吸引到吸引层的共轭类，在向后迭代时也被刻画为不弱吸引到排斥层的共轭类.对于一般的直线，我们证明了定理G，它精确地描述了哪些直线在向前迭代下弱吸引到吸引层，哪些在向后迭代下弱吸引到排斥层。我们还证明了定理H，它给出了弱吸引线的一个统一形式。v3：包含引理2.19的更强证明（定理G的证明的一部分），以供进一步应用。
英文摘要：
This is the third in a series of four papers (with research announcement posted on this arXiv) that develop a decomposition theory for subgroups of $\text{Out}(F_n)$. In this paper, given an outer automorphism of $F_n$ and an attracting-repelling lamination pair, we study which lines and conjugacy classes in $F_n$ are weakly attracted to that lamination pair under forward and backward iteration respectively. For conjugacy classes, we prove Theorem F from the research annoucement, which exhibits a unique vertex group system called the "nonattracting subgroup system" having the property that the conjugacy classes it carries are characterized as those which are not weakly attracted to the attracting lamination under forward iteration, and also as those which are not weakly attracted to the repelling lamination under backward iteration. For lines in general, we prove Theorem G that characterizes exactly which lines are weakly attracted to the attracting lamination under forward iteration and which to the repelling lamination under backward iteration. We also prove Theorem H which gives a uniform version of weak attraction of lines. v3: Contains a stronger proof of Lemma 2.19 (part of the proof of Theorem G) for purposes of further applications.
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