法雷树与怀特黑德链补空间的纤维化
The Farey tree and fibrations of the Whitehead link complement
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中文总结 AI 辅助
研究怀特黑德链补空间纤维化与动力强迫关系，建立其与环面上‘简单轨道对’集的对应，对应有理数法雷树序，通过明确单值化描述来证明。
中文摘要 AI 辅助
我们展示了动力强迫的一个例子（一个动力系统中一个周期轨道的存在迫使其他周期轨道的存在）与三维流形不同纤维化的存在之间的奇特联系。具体而言，我们在怀特黑德链补空间的纤维化与环面上的‘简单轨道对’集之间建立了一一对应。轨道集配备了来自动力强迫关系的全序，这对应于有理数的法雷树序。这与怀特黑德链的纤维化锥上有理点的顺序相对应。为了证明，我们得到了怀特黑德链补空间不同纤维化的所有单值化的明确描述。
英文摘要
We show a curious connection between an example of dynamical forcing, where an existence of one periodic orbit for a dynamical system forces the existence of other periodic orbits, and the existence of different fibrations of a 3 dimensional manifold. Specifically, we establish a one to one correspondence between fibrations of the Whitehead link complement and the set of `simple orbit pairs' on the torus. The set of orbits is equipped with a complete order coming from a dynamical forcing relation, that corresponds to the Farey tree order of rational numbers. This corresponds to the order of the rational point on a fibered cone of the Whitehead link. For the proof we obtain an explicit description of all monodromies of the different fibrations of the Whitehead link complement.
