  We show that any 4-manifold admitting a $(g;k_1,k_2,0)$-trisection is an
irregular 3-fold cover of the 4-sphere whose branching set is a surface in
$S^4$, smoothly embedded except for one singular point which is the cone on a
link. A 4-manifold admits such a trisection if and only if it has a handle
decomposition with no 1-handles; it is conjectured that all simply-connected
4-manifolds have this property.
