论文标题
在特殊的理性同源球的特殊通用图中，将欧几里得空间
On special generic maps of rational homology spheres into Euclidean spaces
论文作者
论文摘要
特殊的通用图是光滑的歧管之间的平滑地图，只有确定的折叠点作为其奇异性。 $ n $ n $ - manifold是否承认欧几里得$ p $ -p $ 1 \ leq p \ leq n $的特殊通用地图是由包括burlet，de Rham，de Rham，Porto，Furuya，Furuya，furuya，furuya，furuya，Seeki，Saeki和Sakakuma的几位作者的。在本文中，我们研究了合理同源性$ n $ -spheres，这些$ n $ spheres将特殊的通用映射纳入$ \ mathbb {r}^{p} $ for $ p <n $。我们使用Stein分解的技术来得出对于存在奇数$ n $的这种地图的必要同源条件。我们检查了我们的条件，包括镜头空间，包括镜头的镜头和总空间$ s^{3} $ - 捆绑$ s^{4} $，并获得有关（非）存在特殊通用图的新结果。
Special generic maps are smooth maps between smooth manifolds with only definite fold points as their singularities. The problem of whether a closed $n$-manifold admits a special generic map into Euclidean $p$-space for $1 \leq p \leq n$ was studied by several authors including Burlet, de Rham, Porto, Furuya, Èliašberg, Saeki, and Sakuma. In this paper, we study rational homology $n$-spheres that admit special generic maps into $\mathbb{R}^{p}$ for $p<n$. We use the technique of Stein factorization to derive a necessary homological condition for the existence of such maps for odd $n$. We examine our condition for concrete rational homology spheres including lens spaces and total spaces of linear $S^{3}$-bundles over $S^{4}$, and obtain new results on the (non-)existence of special generic maps.
