“Slicing” the Hopf link. (English) Zbl 1321.57025

Author’s abstract: A link in the 3-sphere is called (smoothly) slice if its components bound disjoint smoothly embedded disks in the 4-ball. More generally, given a 4-manifold \(M\) with a distinguished circle in its boundary, a link in the 3-sphere is called \(M\)-slice if its components bound in the 4-ball disjoint embedded copies of \(M\). A 4-manifold \(M\) is constructed such that the Borromean rings are not \(M\)-slice but the Hopf link is. This contrasts the classical link-slice setting where the Hopf link may be thought of as “the most nonslice” link. Further examples and an obstruction for a family of decompositions of the 4-ball are discussed in the context of the A-B slice problem.
Reviewer: Ioan Pop (Iaşi)


57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010)
57M25 Knots and links in the \(3\)-sphere (MSC2010)
57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
Full Text: DOI arXiv


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