SPECIAL GENERIC MAPS ON OPEN 4-MANIFOLDS

We characterize those smooth 1-connected open 4-manifolds with certain finite type properties which admit proper special generic maps into 3-manifolds. As a corollary, we show that a smooth 4-manifold homeomorphic to R-4 admits a proper special generic map into R-n for some n = 1, 2 or 3 if and only if it is diffeomorphic to R-4. We also characterize those smooth 4-manifolds homeomorphic to L x R for some closed orientable 3-manifold L which admit proper special generic maps into R-3.