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Izvestiya: Mathematics, 2021, Volume 85, Issue 3, Pages 407–420
DOI: https://doi.org/10.1070/IM9081
(Mi im9081)
 

Plane algebraic curves in fancy balls

N. G. Kruzhilin, S. Yu. Orevkov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
References:
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 smooth embedded 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 are strong $\mathbb{C}$-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 at most five crossings.
Keywords: quasipositive link, $\mathbb C$-boundary, Thom conjecture.
Funding agency Grant number
Russian Science Foundation 19-11-00316
This work was supported by the Russian Science Foundation (project no. 19-11-00316).
Received: 29.06.2020
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2021, Volume 85, Issue 3, Pages 73–88
DOI: https://doi.org/10.4213/im9081
Bibliographic databases:
Document Type: Article
UDC: 515.162.8
Language: English
Original paper language: Russian
Citation: N. G. Kruzhilin, S. Yu. Orevkov, “Plane algebraic curves in fancy balls”, Izv. RAN. Ser. Mat., 85:3 (2021), 73–88; Izv. Math., 85:3 (2021), 407–420
Citation in format AMSBIB
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\by N.~G.~Kruzhilin, S.~Yu.~Orevkov
\paper Plane algebraic curves in fancy balls
\jour Izv. RAN. Ser. Mat.
\yr 2021
\vol 85
\issue 3
\pages 73--88
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\crossref{https://doi.org/10.4213/im9081}
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\jour Izv. Math.
\yr 2021
\vol 85
\issue 3
\pages 407--420
\crossref{https://doi.org/10.1070/IM9081}
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  • https://www.mathnet.ru/eng/im9081
  • https://doi.org/10.1070/IM9081
  • https://www.mathnet.ru/eng/im/v85/i3/p73
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    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    English version PDF:28
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    References:33
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