具有简单结构的特殊一般映射的象的拓扑与可微结构
The topologies and the differentiable structures of the images of special generic maps having simple structures
摘要：
特殊的一般地图是光滑的地图在每个奇点，我们可以表示为$(x_1, \cdots, x_m) \mapsto (x_1,\cdots,x_{n-1},\sum_{k=n}^{m}{x_k}^2)$为适当的坐标。在同伦球面和单位球面上的正则投影上具有两个奇点的Morse函数是特殊的通性。已知它们在各种情况下限制流形的拓扑和可微结构。另一方面，各种流形都承认这样的映射。本文首先给出了$7$维流形上的一个特殊的一般映射及其象。这一结果似乎也提出了一个新的例子，$7$维封闭和单连通流形具有非零三重Massey产品，似乎是一个新的工作有关的Dranishnikov和Rudyak类似的作品。我们还审查结果消失的产品的上同调类，以前获得的作者。特殊类属映射的象是光滑浸入流形，其维数等于目标的维数。作者以前研究了这类映象的拓扑，并对具有简单结构的特殊一般映象的同调群、上同调环及其结构作了新的研究。
英文摘要：
Special generic maps are smooth maps at each singular point of which we can represent as $(x_1, \cdots, x_m) \mapsto (x_1,\cdots,x_{n-1},\sum_{k=n}^{m}{x_k}^2)$ for suitable coordinates. Morse functions with exactly two singular points on homotopy spheres and canonical projections of unit spheres are special generic. They are known to restrict the topologies and the differentiable structures of the manifolds in various situations. On the other hands, various manifolds admit such maps. This article first presents a special generic map on a $7$-dimensional manifold and the image. This results also seems to present a new example of $7$-dimensional closed and simply-connected manifolds having non-vanishing triple Massey products and seems to be a new work related to similar works by Dranishnikov and Rudyak. We also review results on vanishing of products of cohomology classes, previously obtained by the author. The images of special generic maps are smoothly immersed manifolds whose dimensions are equal to the dimensions of the targets. The author studied the topologies of these images previously and studies on homology groups, cohomology rings and structures of them for special generic maps having simple structures are presented as new results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
