Abstract
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.
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