论文标题
小学类的特殊通用图的图像
The images of special generic maps of an elementary class
论文作者
论文摘要
一类特殊通用地图包含具有两个单数点的摩尔斯函数，从拓扑上表征球体，这不是$ 4 $维的，而$ 4 $维二维单位球体。该类用于此类功能的更高维度版本。单位球体的规范投影是最简单的示例，并且与表示为连接的球体产物总和的合适歧管差异为允许这样的地图。已经发现它们强烈限制了流形的拓扑结构和可区分结构。 本文重点介绍了封闭歧管上特殊通用图的图像。它们是平滑沉浸的紧凑型歧管，其尺寸与目标的尺寸相同。一些研究表明，他们有很多有关同源组和共同学环的信息。我们通过研究图像提出了新的结构和明确的示例，本文本质上基本上是关于浸入式紧凑型歧管的结构和明确的代数拓扑和差异拓扑研究。
The class of special generic maps contains Morse functions with exactly two singular points, characterizing spheres topologically which are not $4$-dimensional and the $4$-dimensional unit sphere. This class is for higher dimensional versions of such functions. Canonical projections of unit spheres are simplest examples and suitable manifolds diffeomorphic to ones represented as connected sums of products of spheres admit such maps. They have been found to restrict the topologies and the differentiable structures of the manifolds strongly. The present paper focuses on images of special generic maps on closed manifolds. They are smoothly immersed compact manifolds whose dimensions are same as those of the targets. Some studies imply that they have much information on homology groups and cohomology rings. We present new construction and explicit examples of special generic maps by investigating the images and the present paper is essentially on construction and explicit algebraic topological and differential topological studies of immersed compact manifolds.
