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

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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.