Geodesic
Special generic maps on open 4-manifolds
Journal of Singularities, Tome 1 (2010), pp. 1-12

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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.
DOI : 10.5427/jsing.2010.1a
Classification : 57N13, 57R45, 57R55, 58K15 
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     author = {Osamu Saeki},
     title = {Special generic maps on open 4-manifolds},
     journal = {Journal of Singularities},
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     publisher = {mathdoc},
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     year = {2010},
     doi = {10.5427/jsing.2010.1a},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2010.1a/}
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Osamu Saeki. Special generic maps on open 4-manifolds. Journal of Singularities, Tome 1 (2010), pp. 1-12. doi: 10.5427/jsing.2010.1a

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