  We prove that the canonical 4-dimensional surgery problems can be solved
after passing to a double cover. This contrasts the long-standing conjecture
about the validity of the topological surgery theorem for arbitrary fundamental
groups (without passing to a cover). As a corollary, the surgery conjecture is
reformulated in terms of the existence of free involutions on a certain class
of 4-manifolds. We consider this question and analyze its relation to the
A,B-slice problem.
