论文标题
镜头空间中的代数链接
Algebraic links in lens spaces
论文作者
论文摘要
镜头空间$ l_ {p，q} $是$ \ mathbb {z} _ {p} $ - 在三个球体上的操作。我们研究了在此操作下不变的两个复杂变量的多项式，因此在$ l_ {p，q} $中定义了链接。我们研究这些链接的属性及其与经典代数链接的关系。我们证明，透镜空间中的所有代数链接都是纤维，并获得有关其Seifert属的结果。我们在镜头空间中发现了一些代数结的示例，镜头空间中的升降机是$ 3 $ -sphere的升降机。
The lens space $L_{p,q}$ is the orbit space of a $\mathbb{Z}_{p}$-action on the three sphere. We investigate polynomials of two complex variables that are invariant under this action, and thus define links in $L_{p,q}$. We study properties of these links, and their relationship with the classical algebraic links. We prove that all algebraic links in lens spaces are fibered, and obtain results about their Seifert genus. We find some examples of algebraic knots in lens spaces, whose lift in the $3$-sphere is a torus link.
