Special generic maps on open 4-manifolds

Journal of Singularities
volume 1 (2010), 1-12

Received 16 June 2009. Received in revised form 30 November 2009.

DOI: 10.5427/jsing.2010.1a

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Abstract:

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.

Keywords:

Proper special generic map, differentiable structure, open 4-manifold, end

Mathematical Subject Classification:

Primary 57N13; Secondary 57R45,57R55, 58K15

Author(s) information:

Osamu Saeki
Faculty of Mathematics
Kyushu University
Motooka 744, Nishi-ku, Fukuoka 819-0395, Japan
email: saeki@math.kyushu-u.ac.jp