论文标题
两个手柄属边界中的原始，适当的功率和Seifert曲线
Primitive, proper power, and Seifert curves in the boundary of a genus two handlebody
论文作者
论文摘要
如果在$α$沿$ h $添加2 hangeby $ h $的边界的一个简单的封闭曲线$α$是原始的。如果沿$α$添加2个手柄到$ h $会产生塞菲尔特纤维的空间而不是固体圆环，则曲线称为seifert。如果$α$与$ h $中的基本分离磁盘不相交，则不在$ h $中绑定磁盘，并且在$ h $中不是原始的，据说它是适当的功率。 作为$ s^3 $双曲原始/塞弗特结的分类项目的背景论文之一，其完整列表在[BK20]中给出，本文根据R-R图的原始，适当的功率和Seifert曲线进行了分类。换句话说，我们提供了此类曲线的所有可能的R-R图。此外，我们进一步将适当的功率曲线的所有可能的R-R图分类，相对于任意的完整切割磁盘的两个手柄属的切割磁盘。
A simple closed curve $α$ in the boundary of a genus two handlebody $H$ is primitive if adding a 2-handle to $H$ along $α$ yields a solid torus. If adding a 2-handle to $H$ along $α$ yields a Seifert-fibered space and not a solid torus, the curve is called Seifert. If $α$ is disjoint from an essential separating disk in $H$, does not bound a disk in $H$, and is not primitive in $H$, then it is said to be proper power. As one of the background papers of the classification project of hyperbolic primitive/Seifert knots in $S^3$ whose complete list is given in [BK20], this paper classifies in terms of R-R diagrams primitive, proper power, and Seifert curves. In other words, we provide up to equivalence all possible R-R diagrams of such curves. Furthermore, we further classify all possible R-R diagrams of proper power curves with respect to an arbitrary complete set of cutting disks of a genus two handlebody.
