## A dimension condition on the cohomology of a homogeneous space

The rational cohomology of a homogeneous space G/K admits a homomorphism from H∗(BK) induced from the classifying map G/K→BK of the principal K-bundle G→G/K. Assume the Lie group is K connected, so that π1(BK)=0; then the space G/K is formal in the sense of rational homotopy theory if and only if H∗(G/K) is a free … Read more