论文标题
具有类似同胞戒指的歧管的新家庭承认特殊通用地图
New families of manifolds with similar cohomology rings admitting special generic maps
论文作者
论文摘要
正如Reeb的定理所显示的那样，莫尔斯在封闭的歧管上完全具有两个单数点的摩尔斯功能非常简单且重要。他们表征了尺寸不超过$ 4 $的球体，而$ 4 $维的单位球体。 特殊的通用图是这些地图的通用版本。单位球体的规范预测是特殊的通用。自1990年代以来对Saeki和Sakuma的研究，其次是Nishioka和Wrazidlo，表明球体的可区分结构和流形的同源组（在几个类中）受到限制。我们看到特殊的通用地图很有吸引力。 我们的论文研究了承认此类地图的歧管的共同体环。作为我们的新结果，我们发现了一个新的流形家族，其共同学环相似，并发现（非）特殊通用图的存在与拓扑密切相关。更明确地，我们以前已经发现了相关的家庭，而我们的新歧管则增加了这些发现。
As Reeb's theorem shows, Morse functions with exactly two singular points on closed manifolds are very simple and important. They characterize spheres whose dimensions are not $4$ topologically and the $4$-dimensional unit sphere. Special generic maps are generalized versions of these maps. Canonical projections of unit spheres are special generic. Studies of Saeki and Sakuma since the 1990s, followed by Nishioka and Wrazidlo, show that the differentiable structures of the spheres and the homology groups of the manifolds (in several classes) are restricted. We see special generic maps are attractive. Our paper studies the cohomology rings of manifolds admitting such maps. As our new result, we find a new family of manifolds whose cohomology rings are similar and find that the (non-)existence of special generic maps are closely related to the topologies. More explicitly, we have previously found related families and our new manifolds add to these discoveries.
