论文标题
一般的7维封闭和简单连接的旋转歧管上的折叠图的新明确构造
New explicit construction of fold maps on general 7-dimensional closed and simply-connected spin manifolds
论文作者
论文摘要
在代数拓扑中的中心和显式对象以及较高尺寸闭合和简单连接的歧管的差异拓扑中的中心和显式对象，7维封闭和简单地连接的歧管具有吸引力，尤其是在1950年代 - 60年代积极研究。 米尔诺（Milnor）发现所谓的奇特球体，开始了对这些$ 7 $维的歧管的有吸引力的研究。它影响了通过代数和抽象对象对更高维度封闭和简单相连的流形的理解。最近，通过来自代数拓扑的更具体的概念来研究该类别的班级，例如Crowley，Kreck等的混凝土界异教理论。 作为一种新的基本和重要研究，作者一直在挑战以建设性的方式理解班级的折叠图，这是Morse功能的较高维度版本。本文提出了一种新的通用方法，可以在类的自旋歧管上构建一种方法。
7-dimensional closed and simply-connected manifolds have been attractive as central and explicit objects in algebraic topology and differential topology of higher dimensional closed and simply-connected manifolds, which were studied actively especially in the 1950s--60s. Attractive studies of the class of these $7$-dimensional manifolds were started by the discovery of so-called exotic spheres by Milnor. It has influenced on the understanding of higher dimensional closed and simply-connected manifolds via algebraic and abstract objects. Recently this class is studied via more concrete notions from algebraic topology such as concrete bordism theory by Crowley, Kreck, and so on. As a new kind of fundamental and important studies, the author has been challenging understanding the class in constructive ways via construction of fold maps, which are higher dimensional versions of Morse functions. The present paper presents a new general method to construct ones on spin manifolds of the class.
