论文标题
在大约7美元的封闭式封闭式和简单连接的歧管上，将折叠地图绕过飞机
Round fold maps into the plane on some $7$-dimensional closed and simply-connected manifolds
论文作者
论文摘要
圆形图是封闭的歧管上的平滑地图，在封闭的歧管上，局部表示为莫尔斯函数的乘积图和开放磁盘上的身份图，其奇异性被实现为浓嵌入的球体。作者先前引入了这样的地图。我们的论文在约7美元的简单相互连接的流形上展示了圆形地图，其共同体戒指与$ 2 $维的复杂投射空间和3美元的二维型球体的产物是同构的。作者先前已经研究了这些歧管上的旋转歧管上的旋转歧管上精确研究了这种歧管。这些流形构成了Higehr维度封闭和简单相互连接的显式类别，它们是经典代数拓扑和差异拓扑中的中心对象。以几何和建设性的方式理解这些歧管仍然很有吸引力，我们认为这是先驱。 折叠图被定义为平滑的地图，在局部表示摩尔斯函数的乘积图和开放磁盘上的身份图。它们是莫尔斯功能理论和对流形的几何形状的应用理论的基本和强大的工具。即使在基本或众所周知的歧管上，折叠图的明确结构也很困难，而我们可以知道Eliashberg庆祝理论的（非）存在于1970年代，并且在相当多的情况下是相关的。
Round fold maps are smooth maps on closed manifolds which are locally represented as the product maps of Morse functions and identity maps on open disks and whose singularity is realized as concentrically embedded spheres. The author previously introduced such maps. Our paper presents round fold maps on some $7$-dimensional simply-connected manifolds whose cohomology rings are isomorphic to that of the product of the $2$-dimensional complex projective space and a $3$-dimensional sphere. Such manifolds have been studied precisely by Wang and round fold maps on spin manifolds in these manifolds have been previously studied by the author. These manifolds form explicit classes of higehr dimensional closed and simply-connected manifolds, which are central objects in classical algeberic topology and differential topology. Understanding these manifolds in geometric and constructive ways is still attractive, which we think as pioneers. Fold maps are defined as smooth maps which are locally represented as the product maps of Morse functions and identity maps on open disks. They are fundamental and strong tools in generalizations of theory of Morse functions and applications to geometry of manifolds. Explicit construction of fold maps are difficult even on elementary or well-known manifolds whereas we can know the (non-)existence from Eliashberg's celebrating theory in the 1970s and related one in considerable cases.
