  A link in the 3-sphere is homotopically trivial, according to Milnor, if its
components bound disjoint maps of disks in the 4-ball. This paper concerns the
question of what spaces give rise to the same class of homotopically trivial
links when used in place of disks in an analogous definition. We show that
there are 4-manifolds for which this property depends on their embedding in the
4-ball. This work is motivated by the A-B slice problem, a reformulation of the
4-dimensional topological surgery conjecture. As a corollary this provides a
new, secondary, obstruction in the A-B slice problem for a certain class of
decompositions of D^4.
