|
Plane algebraic curves in fancy balls
N. G. Kruzhilin, S. Yu. Orevkov Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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.
Received: 29.06.2020
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
Linking options:
https://www.mathnet.ru/eng/im9081https://doi.org/10.1070/IM9081 https://www.mathnet.ru/eng/im/v85/i3/p73
|
Statistics & downloads: |
Abstract page: | 367 | Russian version PDF: | 65 | English version PDF: | 28 | Russian version HTML: | 139 | References: | 33 | First page: | 20 |
|