花式球中的平面代数曲线
Plane algebraic curves in fancy balls
摘要：
Boileau和Rudolph称$3$ -球中的链$L$为$\bf C$ -边界，如果它可以实现为$\bf C^2$中的代数曲线$A$与光滑嵌入的$4$ -球$B$的边界的交点。他们表明，有些链接不是$\bf C$ -边界。如果$A\setminus B$是连通的，我们称$L$是强$\bf C$ -边界.特别地，所有拟正链都是强$\bf C$ -边界.本文给出了非拟正强$\bf C$ -边界和非强$\bf C$ -边界的例子。给出了至多5个交叉点的（强）$\bf C$ -边界的完全分类.
英文摘要：
Boileau and Rudolph called a link $L$ in the $3$-sphere a $\bf C$-boundary if it can be realized as the intersection of an algebraic curve $A$ in $\bf C^2$ with the boundary of a smooth embedded $4$-ball $B$. They showed that some links are not $\bf C$-boundaries. We say that $L$ is a strong $\bf C$-boundary if $A\setminus B$ is connected. In particular, all quasipositive links are strong $\bf C$-boundaries. In this paper we give examples of non-quasipositive strong $\bf C$-boundaries and non-strong $\bf C$-boundaries. We give a complete classification of (strong) $\bf C$-boundaries with at most 5 crossings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
