论文标题
零属，3元素的纤维链接$ s^3 $
The genus zero, 3-component fibered links in $S^3$
论文作者
论文摘要
通过接触几何形状的镜头，已经完全理解了一对裤子的页面的开放式书籍分解。本说明的目的是在形成其绑定和相应的单粒子的链接方面表现出对此类开放书籍的分类的纯粹拓扑衍生。我们从最简单的示例中构造了所有链接及其对裤子纤维表面，即通过执行（广义）失速的两个HOPF链接的连接总和。然后，通过在$ s^3 $中应用两个属的属属理论，我们验证了该家族中链接的单粒粒子是唯一对应于$ s^3 $的裤子的开放书籍分解的唯一一个。
The open book decompositions of the 3-sphere whose pages are pairs of pants have been fully understood for some time, through the lens of contact geometry. The purpose of this note is to exhibit a purely topological derivation of the classification of such open books, in terms of the links that form their bindings and the corresponding monodromies. We construct all of the links and their pair-of-pants fiber surfaces from the simplest example, a connected sum of two Hopf links, through performing (generalized) Stallings twists. Then, by applying the now-classical theory of genus two Heegaard diagrams in $S^3$, we verify that the monodromies of the links in this family are the only ones corresponding to pair-of-pants open book decompositions of $S^3$.
