论文标题
在7维封闭和简单连接的新类上的显式折叠图
Explicit fold maps on 7-dimensional closed and simply-connected spin manifolds of new classes
论文作者
论文摘要
封闭的（和简单连接的）歧管大于4的歧管通过复杂的代数和抽象理论进行分类，例如手术理论和同义理论。很难以这种方式处理3或4维闭合歧管。但是，后一种通过几何和建设性方式工作并不难。例如，尺寸不高的假设使我们能够通过图表处理歧管。尽管自然而重要，但很难以这些方式研究更高的维歧管。 在本文中，我们通过{\ it折叠}地图介绍了此类研究，这些图是Morse功能的较高维数。作者先前在7维闭合和简单连接的歧管上构建了折叠图，以满足同系环的其他条件，包括所谓的{\ it Exotic}同型球体。本文涉及更广泛类的这种歧管上的折叠地图。
Closed (and simply-connected) manifolds whose dimensions are greater than 4 are classified via sophisticated algebraic and abstract theory such as surgery theory and homotopy theory. It is difficult to handle 3 or 4-dimensional closed manifolds in such ways. However, the latter work via geometric and constructive ways is not so difficult. The assumption that the dimensions are not high enables us to handle the manifolds via diagrams for example. It is difficult to study higher dimensional manifolds in these ways, although it is natural and important. In the present paper, we present such studies via {\it fold} maps, which are higher dimensional variants of Morse functions. The author previously constructed fold maps on 7-dimensional closed and simply-connected manifolds satisfying additional conditions on cohomology rings, including so-called {\it exotic} homotopy spheres. This paper concerns fold maps on such manifolds of a wider class.
