On Real Cohomology Generators of Compact Homogeneous Spaces

In this paper we discuss the degrees of real cohomology generators of compact homogeneous spaces. We relate these degrees to rational homotopy groups and, furthermore, we discuss the formality and geometric formality of compact homogeneous spaces in the light of their cohomology generators. For generalized symmetric spaces the explicit formulas are obtained. 2000 Mathematics Subject Classification. 53C25, 57R57, 58A14, 57R17