论文标题
关于$ s^3 $的p/p和p/sf结的非输血
On nonhyperbolicity of P/P and P/SF knots in $S^3$
论文作者
论文摘要
在[B90]或可用版本[B18]中，Berge构建了十二个原始/primitve（或简单p/p）结的家庭，被称为Berge结。在[B08]中或在[G13]中独立证明，所有P/P结都是Berge结，它给出了P/P结的完整分类。但是，在[B90]中不确定了Berge结的双曲线。作为P/P结的自然概括，Dean以$ S^3 $引入了原始/Seifert（或简单的P/SF）结。双曲线P/SF结的分类已经进行了，并在[BK20]中给出了双曲P/SF结的完整列表。 在本文中，我们为p/p或p/sf节提供了必要的，足够或等效的条件是非流血的，并且它们在某些p/sf节上的应用。本文的结果将用于[K20A]中P/P和P/SF结的双曲线，并分别在[B90]和[BK20]中分别完成双曲线P/P和P/SF结的分类。
In [B90] or an available version [B18], Berge constructed twelve families of primitive/primitve(or simply P/P) knots, which are referred to as the Berge knots. It is proved in [B08] or independently in [G13] that all P/P knots are the Berge knots, which gives the complete classification of P/P knots. However, the hyperbolicity of the Berge knots was undetermined in [B90]. As a natural generalization of P/P knots, Dean introduced primitive/Seifert(or simply P/SF) knots in $S^3$. The classification of hyperbolic P/SF knots has been performed and the complete list of hyperbolic P/SF knots is given in [BK20]. In this paper, we provide necessary, sufficient, or equivalent conditions for P/P or P/SF knots being nonhyperbolic, and their applications on some P/SF knots. The results of this paper will be used in proving the hyperbolicity of P/P and P/SF knots in [K20a] and [K20b] completing the classification of hyperbolic P/P and P/SF knots in [B90] and [BK20] respectively.
