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Plane algebraic curves in fancy balls
Izvestiya: Mathematics ( IF 0.8 ) Pub Date : 2021-07-08 , DOI: 10.1070/im9081 N. G. Kruzhilin 1 , S. Yu. Orevkov 1
中文翻译:
花式球中的平面代数曲线
更新日期:2021-07-08
Izvestiya: Mathematics ( IF 0.8 ) Pub Date : 2021-07-08 , DOI: 10.1070/im9081 N. G. Kruzhilin 1 , S. Yu. Orevkov 1
Affiliation
Boileau and Rudolph [1] called an oriented link in the 3-sphere a -boundary if it can be realized as the intersection of an algebraic curve in and the boundary of a smooth embedded closed 4-ball . They showed that some links are not -boundaries. We say that is a strong -boundary if is connected. In particular, all quasipositive links are strong -boundaries.
In this paper we give examples of non-quasipositive strong -boundaries and non-strong -boundaries. We give a complete classification of (strong) -boundaries with at most five crossings.
中文翻译:
花式球中的平面代数曲线
布瓦洛和鲁道夫[1]被称为定向链路在三维球面一个 -boundary如果它可以被实现为代数曲线的交点在和一个平滑嵌入的边界关闭4-球。他们表明某些链接不是边界。如果是连通的,我们说这是一个强 边界。特别是,所有准正链接都是强边界。
在本文中,我们给出了非拟正强边界和非强边界的例子。我们给出了最多五个交叉点的(强)边界的完整分类。