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Given a link
, we ask
whether the components of
bound disjoint, nullhomologous disks properly embedded in a simply connected positive-definite
smooth
–manifold;
the knot case has been studied extensively by Cochran, Harvey and Horn. Such a
–manifold
is necessarily homeomorphic to a (punctured)
.
We characterize all links that are slice in a (punctured)
in
terms of ribbon moves and an operation which we call adding a generalized positive
crossing. We find obstructions in the form of the Levine–Tristram signature function,
the signs of the first author’s generalized Sato–Levine invariants, and certain Milnor’s
invariants. We show that the signs of coefficients of the Conway polynomial obstruct a
–component link from being
slice in a single punctured
and conjecture these are obstructions in general. These results have applications to the question of when
a
–manifold bounds a
–manifold whose intersection
form is that of some
.
For example, we show that any homology
–sphere is
cobordant, via a smooth positive-definite manifold, to a connected sum of surgeries on
knots in
.