论文标题
不良3孔的结构定理
A Structure Theorem for Bad 3-Orbifolds
论文作者
论文摘要
我们明确构建了不良3孔的集合，\（\ Mathcal {x} \），满足以下属性： \开始{枚举} \项目任何\（x \ in \ mathcal {x} \）的基础拓扑空间是同型对$ s^2 \ times i $或$（s^2 \ times s^1）\ backslash b^3 $。 \ item \（x \ in \ Mathcal {x} \）的边界由一个或两个球形2个器组成。 \ item，通过重复多次，以下操作，从一个好的3孔口中获得任何不良的3-孔。 \ end {枚举} 相反，任何不良的3- orbifold \（\ oo \）都包含一些\（x \ in \ Mathcal {x} \）作为sub-orbifold;我们调用删除\（x \）并限制所得边界\ em cut and-cap。
We explicitly construct a collection of bad 3-orbifolds, \(\mathcal{X}\), satisfying the following properties: \begin{enumerate} \item The underlying topological space of any \(X \in \mathcal{X}\) is homeomorphic to $S^2\times I$ or $(S^2\times S^1)\backslash B^3$. \item The boundary of any \(X \in \mathcal{X}\) consists of one or two spherical 2-orbifolds. \item Any bad 3-orbifold is obtained from a good 3-orbifold by repeating, finitely many times, the following operation: remove one or two orbifold-balls, and glue in some \(X \in \mathcal{X}\). \end{enumerate} Conversely, any bad 3-orbifold \(\OO\) contains some \(X \in \mathcal{X}\) as a sub-orbifold; we call removing \(X\) and capping the resulting boundary \em cut-and-cap.\em\ Then by cutting-and-capping finitely many times we obtain a good orbifold.
