论文标题
特殊通用图限制为$ {\ MATHBB {r}}^5 $ on $ 6 $ - 维度或更高维度的封闭且简单地连接的歧管
Restrictions on special generic maps into ${\mathbb{R}}^5$ on $6$-dimensional or higher dimensional closed and simply-connected manifolds
论文作者
论文摘要
一类特殊的通用图是一类天然的平滑地图，其中包含摩尔斯的功能，这些函数恰好是两个单一点和单位球体的规范投影。我们在此类地图上发现了$ 6 $维或更高维的封闭式和简单连接的歧管的新限制，以$ {\ mathbb {r}}^5 $。 对单位球体没有差异的球并不承认在相当多的情况下编成阴性的地图。他们限制了一般流形的同质形态和差异类型。另一方面，某些基本流形将特殊的通用图接收到合适的欧几里得空间中：表示为单位球体产品的连接产品总和的歧管就是这样的例子。这促使我们研究了（非）在基本流形（例如投影空间）以及一些封闭和简单相关的歧管上的特殊通用图。例如，在我们的新研究中，新的研究戒指的新显式调查是钥匙。
The class of special generic maps is a natural class of smooth maps containing Morse functions on spheres with exactly two singular points and canonical projections of unit spheres. We find new restrictions on such maps on $6$-dimensional or higher dimensional closed and simply-connected manifolds into ${\mathbb{R}}^5$. Spheres which are not diffeomorphic to unit spheres do not admit such maps whose codimensions are negative in considerable cases. They restrict the homeomorphism and the diffeomorphism types of the manifolds in general. On the other hands, some elementary manifolds admit special generic maps into suitable Euclidean spaces: manifolds represented as connected sums of products of unit spheres are of such examples. This motivates us to study the (non-)existence of special generic maps on elementary manifolds such as projective spaces and some closed and simply-connected manifolds. For example, new explicit investigations of cohomology rings are keys in our new study.
