Plane algebraic curves in fancy balls

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...

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Bibliographic Details
Published in:Izvestiya. Mathematics 2021-06, Vol.85 (3), p.407-420
Main Authors: Kruzhilin, N. G., Orevkov, S. Yu
Format: Article
Language:English
Subjects:
Algebra
Boundaries
mathbb C$-boundary
quasipositive link
Thom conjecture
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Summary: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.
ISSN:1064-5632
1468-4810
DOI:10.1070/IM9081