Plane algebraic curves in fancy balls

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Boileau and Rudolph [1] called an oriented link $L$ in the 3-sphere a \textit{$\mathbb{C}$-boundary} if it can be realized as the intersection of an algebraic curve $A$ in $\mathbb{C}^2$ and the boundary of a smoothembedded closed 4-ball $B$. They showed that some links are not $\mathbb{C}$-boundaries. We say that $L$is a \textit{strong $\mathbb{C}$-boundary} if $A\setminus B$ is connected. In particular, all quasipositive links arestrong $\mathbb{C}$-boundaries.In this paper we give examples of non-quasipositive strong $\mathbb{C}$-boundaries and non-strong$\mathbb{C}$-boundaries. We give a complete classification of (strong) $\mathbb{C}$-boundaries with atmost five crossings.

作者简介

Nikolai Kruzhilin

Steklov Mathematical Institute of Russian Academy of Sciences

Email: kruzhil@mi-ras.ru
Doctor of physico-mathematical sciences

Stepan Orevkov

Steklov Mathematical Institute of Russian Academy of Sciences

Email: orevkov@math.ups-tlse.fr
Candidate of physico-mathematical sciences, Senior Researcher

参考

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版权所有 © Kruzhilin N.G., Orevkov S.Y., 2021

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