论文标题
在$ 3 $二维复杂的投影空间上，特殊通用地图不存在的证明
Proofs of the non-existence of special generic maps on the $3$-dimensional complex projective space
论文作者
论文摘要
我们证明了在$ 3 $维的复杂投影空间上的特殊通用地图不存在，作为我们的新结果，并通过几种方法进行推论。 特殊的通用图是摩尔斯函数的概括，在球体上恰好有两个奇异点，而单位球体的规范投影是特殊的通用。我们的论文重点介绍了包含$ 3 $维的复杂投影空间的封闭式和简单连接的歧管上的地图。 众所周知，承认特殊通用图的球体的可区分结构受到强烈限制。包括作者在内的各个人研究了封闭和简单连接的流形和投射空间的特殊通用地图。 （非）存在和构建是主要问题。关于封闭式和简单连接的流形的此类地图的研究很难大于$ 5 $。
We prove the non-existence of special generic maps on $3$-dimensional complex projective space as our new result and a corollary by several methods. Special generic maps are generalizations of Morse functions with exactly two singular points on spheres and canonical projections of unit spheres are special generic. Our paper focuses on such maps on closed and simply-connected manifolds of classes containing the $3$-dimensional complex projective space. The differentiable structures of spheres admitting special generic maps are known to be restricted strongly. Special generic maps on closed and simply-connected manifolds and projective spaces have been studied by various people including the author. The (non-)existence and construction are main problems. Studies on such maps on closed and simply-connected manifolds whose dimensions are greater than $5$ have been difficult.
