  We consider topologically twisted N=4 supersymmetric Yang-Mills theory on a
four-manifold of the form V = W \times R_+ or V = W \times I, where W is a
Riemannian three-manifold. Different kinds of boundary conditions apply at
infinity or at finite distance. We verify that each of these conditions defines
a `middle-dimensional' subspace of the space of all bulk solutions. Taking the
two boundaries of V into account should thus generically give a discrete set of
solutions. We explicitly find the spherically symmetric solutions when W = S^3
endowed with the standard metric. For widely separated boundaries, these
consist of a pair of solutions which coincide for a certain critical value of
the boundary separation and disappear for even smaller separations.
