Studies on rational visibility problems of a Lie Group and extensions of symplectic classes by a model for the evaluation map

我们已经解决了给齐性空间秩为1的简单李群的有理可见性问题。特别是，可见度是明确确定的所有情况下，这样的李群。此外，对于具有辛纤维的纤维化，在2k维环面与纤维有理可分的条件下，讨论了辛形式的上同调类扩张到纤维化全空间的上同调类的一个充要条件.我们的主要工具的研究是沙利文模型的功能空间，由于布朗和Szczarba和合理的模型的评价地图。

We have solved the rational visibility problems of simple Lie groups which give homogeneous spaces of rank one. In particular, the visible degrees are determined explicitly for all the cases of such Lie groups. Moreover, for a fibration with symplectic fibre, we discuss a necessary and sufficient condition for the cohomology class of the symplectic form to extend to a cohomology class of the total space of the fibration provided the 2k-dimensional torus is rationally separable from the fibre. Our main tools for the study are the Sullivan model for a function space due to Brown and Szczarba and a rational model for the evaluation map.