论文标题
通过特殊通用地图来表征某些类别的$ 6 $维
Characterizing certain classes of $6$-dimensional closed and simply-connected manifolds via special generic maps
论文作者
论文摘要
本文为$ 6 $维的封闭式和简单连接的某些类别的流形找到了新的必要条件和足够的条件，以便将特殊的通用地图接收到某些欧几里得空间。 一类特殊的通用地图自然包含摩尔斯的函数，在所谓的Reeb定理中的球体上有两个单数点，从拓扑表征球体，并且是单位球体的规范投影。我们的论文涉及Reeb定理的变体。已知几个结果e。 g。目标歧管的情况是平面和某些域的歧管封闭并简单地连接的情况。我们的论文涉及Nishioka结果的$ 6 $维版本，确定了$ 5 $维的封闭式且简单地连接的歧管，将特殊的通用地图完全纳入欧几里得空间。封闭和简单连接的流形是（经典）代数拓扑和差异拓扑中的中心几何对象。 $ 6 $维情况比$ 5 $维的案例更为复杂：它们是通过显式代数系统分类的。
The present paper finds new necessary and sufficient conditions for $6$-dimensional closed and simply-connected manifolds of certain classes to admit special generic maps into certain Euclidean spaces. The class of special generic maps naturally contains Morse functions with exactly two singular points on spheres in so-called Reeb's theorem, characterizing spheres topologically, and canonical projections of unit spheres. Our paper concerns variants of Reeb's theorem. Several results are known e. g. the cases where the manifolds of the targets are the plane and some cases where the manifolds of the domains are closed and simply-connected. Our paper concerns $6$-dimensional versions of a result of Nishioka, determining $5$-dimensional closed and simply-connected manifolds admitting special generic maps into Euclidean spaces completely. Closed and simply-connected manifolds are central geometric objects in (classical) algebraic topology and differential topology. The $6$-dimensional case is more complicated than the $5$-dimensional one: they are classified via explicit algebraic systems.
