Geodesic
Plane algebraic curves in fancy balls
Izvestiya. Mathematics , Tome 85 (2021) no. 3, pp. 407-420

Voir la notice de l'article provenant de la source Math-Net.Ru

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
Mots-clés : Thom conjecture. 
@article{IM2_2021_85_3_a5,
     author = {N. G. Kruzhilin and S. Yu. Orevkov},
     title = {Plane algebraic curves in fancy balls},
     journal = {Izvestiya. Mathematics },
     pages = {407--420},
     publisher = {mathdoc},
     volume = {85},
     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2021_85_3_a5/}
}
TY  - JOUR
AU  - N. G. Kruzhilin
AU  - S. Yu. Orevkov
TI  - Plane algebraic curves in fancy balls
JO  - Izvestiya. Mathematics 
PY  - 2021
SP  - 407
EP  - 420
VL  - 85
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2021_85_3_a5/
LA  - en
ID  - IM2_2021_85_3_a5
ER  - 
%0 Journal Article
%A N. G. Kruzhilin
%A S. Yu. Orevkov
%T Plane algebraic curves in fancy balls
%J Izvestiya. Mathematics 
%D 2021
%P 407-420
%V 85
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2021_85_3_a5/
%G en
%F IM2_2021_85_3_a5
N. G. Kruzhilin; S. Yu. Orevkov. Plane algebraic curves in fancy balls. Izvestiya. Mathematics , Tome 85 (2021) no. 3, pp. 407-420. http://geodesic.mathdoc.fr/item/IM2_2021_85_3_a5/