论文标题
7维简单连接的自旋歧管，其积分共同的共同体戒指与$ {\ Mathbb {c} p} p}^2 \ times s^3 $ ADGIT圆形折叠映射是同构的
7-dimensional simply-connected spin manifolds whose integral cohomology rings are isomorphic to that of ${\mathbb{C}P}^2 \times S^3$ admit round fold maps
论文作者
论文摘要
我们对以几何和建设性的方式了解7维封闭和简单相互连接的歧管的类别很感兴趣。我们已经在以前的某些歧管上构建了明确的折叠图，它们是莫尔斯功能的较高维度版本。 这些研究是由{\ it特殊通用}地图的研究激发的，莫尔斯在同型球体上的较高维度版本具有两个奇异点，除了$ 4 $维情况外，它们的表征是拓扑。例如，该类包含单位球体的规范投影。 已经发现该类是有趣的，严格限制了歧管的拓扑和可区分结构：Saeki，Sakuma和Wrazidlo发现了明确的现象。 本文涉及$ 7 $维的封闭式和简单连接的旋转歧管上的折叠地图，其整体共同体学环与$ 2 $尺寸的复杂投影空间和$ 3 $二维球体的产物同构。
We have been interested in understanding the class of 7-dimensional closed and simply-connected manifolds in geometric and constructive ways. We have constructed explicit fold maps, which are higher dimensional versions of Morse functions, on some of the manifolds, previously. The studies have been motivated by studies of {\it special generic} maps, higher dimensional versions of Morse functions on homotopy spheres with exactly two singular points, characterizing them topologically except $4$-dimensional cases. The class contains canonical projections of unit spheres for example. This class has been found to be interesting, restricting the topologies and the differentiable structures of the manifolds strictly: Saeki, Sakuma and Wrazidlo found explicit phenomena. The present paper concerns fold maps on $7$-dimensional closed and simply-connected spin manifolds whose integral cohomology rings are isomorphic to that of the product of the $2$-dimensional complex projective space and the $3$-dimensional sphere.
