Special generic maps on open 4-manifolds
Special generic maps on open 4-manifolds
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DOI：
10.5427/jsing.2010.1a
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
O. Saeki
中科院分区：
文献类型：
--
作者：
O. Saeki
我们刻画了具有某些有限型性质的光滑1-连通开4-流形，这些流形允许适当的特殊一般映射到3-流形中。作为推论，我们证明了一个同胚于R4的光滑4-流形允许一个特殊的通有映射到Rn中，其中n = 1，2或3当且仅当它同胚于R4。对于可定向的闭3-流形L，若R ~ 3中有真特殊一般映射，则我们刻划了与L ×R同胚的光滑4-流形。
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 R4 admits a proper special generic map into Rn for some n = 1, 2 or 3 if and only if it is diffeomorphic to R4. We also characterize those smooth 4-manifolds homeomorphic to L ×R for some closed orientable 3-manifold L which admit proper special generic maps into R3.