Plane algebraic curves in fancy balls
- Authors: Kruzhilin N.G.1, Orevkov S.Y.1
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Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences
- Issue: Vol 85, No 3 (2021)
- Pages: 73-88
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/133850
- DOI: https://doi.org/10.4213/im9081
- ID: 133850
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Abstract
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.
Keywords
About the authors
Nikolai Georgievich Kruzhilin
Steklov Mathematical Institute of Russian Academy of Sciences
Email: kruzhil@mi-ras.ru
Doctor of physico-mathematical sciences
Stepan Yur'evich Orevkov
Steklov Mathematical Institute of Russian Academy of Sciences
Email: orevkov@math.ups-tlse.fr
Candidate of physico-mathematical sciences, Senior Researcher
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