  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 "the most non-slice"
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.
