This paper studies
various properties of 3-handle presentations of 1-connected, smooth,
4-manifolds—with—connected-boundary. Although the question of whether or not
such 4-manifolds have handle presentations consisting solely of 0-, 1- and
2-handles remains open, the main results of this paper do imply that the
essential structure of such 4-manifolds is contained in a neighborhood of their
2-skeleton.