  The A-B slice problem is a reformulation of the topological 4-dimensional
surgery conjecture in terms of decompositions of the 4-ball and link homotopy.
We show that link groups, a recently developed invariant of 4-manifolds,
provide an obstruction for the class of model decompositions, introduced by M.
Freedman and X.-S. Lin. This unifies and extends the previously known partial
obstructions in the A-B slice program. As a consequence, link groups satisfy
Alexander duality when restricted to the class of model decompositions, but not
for general submanifolds of the 4-ball.
