论文标题
关于尺寸大于4
Notes on explicit special generic maps into Eulidean spaces whose dimensions are greater than 4
论文作者
论文摘要
特殊的通用图是Morse函数的较高维度版本，具有两个单数点，表征了拓扑表征，除了4维情况和4维标准球体外。此类地图的类还包含单位球体的规范投影。 从代数拓扑和歧管的差异拓扑的角度来看，该类是有趣的。这些地图已被证明可以限制卡拉比，Saeki和Sakuma在2010年代和后来的Nishioka，Wrazidlo和作者强烈限制流形的拓扑结构和可区分结构。所谓的异国情调球体承认，在相当多的情况下没有特殊的通用图，并且同源组和协同学环被证明受到了严格的限制。此外，对欧几里得空间的特殊通用图的尺寸小于或等于4。本文主要涉及目标尺寸大于或等于5的情况。
Special generic maps are higher dimensional versions of Morse functions with exactly two singular points, characterizing spheres topologically except 4-dimensional cases and 4-dimensional standard spheres. The class of such maps also contains canonical projections of unit spheres. This class is interesting from the viewpoint of algebraic topology and differential topology of manifolds. These maps have been shown to restrict the topologies and the differentiable structures of the manifolds strongly by Calabi, Saeki and Sakuma before 2010s, and later Nishioka, Wrazidlo and the author. So-called exotic spheres admit no special generic map in considerable cases and homology groups and cohomology rings are shown to be strongly restricted. Moreover, special generic maps into Euclidean spaces whose dimensions are smaller than or equal to 4 have been studied well. The present paper mainly concerns cases where the dimensions of targets are greater than or equal to 5.
