论文标题
封闭的歧管不承认编辑为负且共同体圈的特殊通用图
Closed manifolds admitting no special generic maps whose codimensions are negative and their cohomology rings
论文作者
论文摘要
特殊的通用图是Morse功能的较高维度版本，具有两个单数点，在拓扑上表征了球体，除了$ 4 $维的情况外：在这些情况下，标准球体的表征。单位球体的规范预测是特殊的通用。在合适的情况下，很容易构建特殊的通用图，例如，以相连的球体总和表示，例如，球体的产物总和。有趣的事实是，这些地图限制了在各种情况下严格承认它们的拓扑结构和可区分结构。例如，在相当多的情况下，对某些欧几里得空间没有特殊的通用图承认，异国情调的球体对标准球没有差异。 总的来说，很难找到（家庭的家庭）承认没有适当班级的地图。本文涉及这项工作的新结果，其中关键对象是歧管同种学类别的产品。我们可以看到，在大量情况下，诸如封闭的象征流形和真实的射击空间之类的歧管都没有在任何连接的NIN锁定歧管中进行特殊的通用图。
Special generic maps are higher dimensional versions of Morse functions with exactly two singular points, characterizing spheres topologically except $4$-dimensional cases: in these cases standard spheres are characterized. Canonical projections of unit spheres are special generic. In suitable cases, it is easy to construct special generic maps on manifolds represented as connected sums of products of spheres for example. It is an interesting fact that these maps restrict the topologies and the differentiable structures admitting them strictly in various cases. For example, exotic spheres, which are not diffeomorphic to standard spheres, admit no special generic map into some Euclidean spaces in considerable cases. In general, it is difficult to find (families of) manifolds admitting no such maps of suitable classes. The present paper concerns a new result on this work where key objects are products of cohomology classes of the manifolds. We can see that manifolds such as closed symplectic manifolds and real projective spaces admit no special generic maps into any connected nin-closed manifold in considerable cases.
