论文标题
同源性与同型在纤维上和限制
Homology versus homotopy in fibrations and in limits
论文作者
论文摘要
由诸如希拉利猜想山口（Yamaguchi）之类的突出问题的动机 - Yokura最近提出了关于纤维，基础和总空间的合理同型和理性共同体组关系的某些估计，并在合理椭圆形空间的振动中。 在本文中，我们在形式椭圆形空间的类别中证明了这些估计值，通常，每当总空间还具有正面的欧拉特征或具有均匀的歧管（分别是已知示例）正截面曲率的合理同型类型时。此外，我们提供近似猜想的一般估计值。 此外，我们建议研究某些渐进剂的理性椭圆空间家族，并从对两个阶段空间的角度讨论了猜想的估计。
Motivated by prominent problems like the Hilali conjecture Yamaguchi--Yokura recently proposed certain estimates on the relations of the dimensions of rational homotopy and rational cohomology groups of fibre, base and total spaces in a fibration of rationally elliptic spaces. In this article we prove these estimates in the category of formal elliptic spaces and, in general, whenever the total space in addition has positive Euler characteristic or has the rational homotopy type of a homogeneous manifold (respectively of a known example) of positive sectional curvature. Additionally, we provide general estimates approximating the conjectured ones. Moreover, we suggest to study families of rationally elliptic spaces under certain asymptotics, and we discuss the conjectured estimates from this perspective for two-stage spaces.
