论文标题
特殊的通用映射到$ {\ Mathbb {r}}^5 $上的封闭式和简单连接的歧管和有关歧管的共同体的信息
Special generic maps into ${\mathbb{R}}^5$ on closed and simply-connected manifolds and information on the cohomology of the manifolds
论文作者
论文摘要
莫尔斯在球体和球体的规范投影上的恰好有两个奇异点的功能属于某种良好的平滑地图类别的类别：特殊的通用图。我们主要调查有关封闭和简单连接的流形的共同体信息，通过研究嵌入式曲线和子曲线及其预先映射，将这些地图承认为$ 5 $维的欧几里得空间。 自1990年代以来，Saeki和Sakuma的同源群体研究（大多数情况下的尺寸低于$ 5 $）的研究（其尺寸低于$ 5 $），后来是Nishioka和Nishioka和Wrazidlo自2010年代以来的开创。最近，作者开始开创有关欧几里得空间尺寸可能不低于$ 5 $的案例的共同体学研究的开创性研究。由于我们认为的歧管尺寸更高的情况，我们的新案例很困难。以前，我们发现了对同种学环的几个限制。我们通过新的调查提出了新的限制。
Morse functions with exactly two singular points on spheres and canonical projections of spheres belong to the class of a certain good class of smooth maps: special generic maps. We mainly investigate information on cohomology of closed and simply-connected manifolds admitting such maps into the $5$-dimensional Euclidean spaces by investigating the embedded curves and submanifolds and their preimages. Studies on homology groups for ones into the Euclidean spaces (whose dimensions are lower than $5$ in most cases) have been pioneered by Saeki and Sakuma since 1990s and later by Nishioka and Wrazidlo since 2010s. Recently the author has started pioneering studies on the cohomology for cases where the dimensions of the Euclidean spaces may not be lower than $5$. Our new cases are difficult due to the situation that the dimensions of manifolds we consider are higher. Previously, we have found several restrictions on the cohomology rings. We present new restrictions by new investigations.
