Journal of Singularities
volume 1 (2010), 1-12
Received 16 June 2009. Received in revised form 30 November 2009.
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.
Proper special generic map, differentiable structure, open 4-manifold, end
Mathematical Subject Classification:
Primary 57N13; Secondary 57R45,57R55, 58K15
Faculty of Mathematics
Motooka 744, Nishi-ku, Fukuoka 819-0395, Japan