On the cohomology of generalized homogeneous spaces (Q2750914)

Generalized homogeneous spaces \(G/H\) are considered such that \(G\) and \(H\) are homotopy equivalent to \(\Omega BG\) and \(\Omega BH\) for path connected spaces \(BG\) and \(BH\), and \(G/H\) is the homotopy fiber of a based map \(f:BH\to BG\).NEWLINENEWLINENEWLINEBy applying Eilenberg-Moore spectral sequences, the authors investigate the similarity between the calculation of the cohomology \(H^*(G/H; R)\) of a generalized homogeneous space \(G/H\) with coefficients in a commutative Noetherian ring \(R\) and the calculation of the cohomology of classical homogeneous spaces of compact Lie groups under the hypothesis that \(H^*(BG; R)\) and \(H^*(BH;R)\) are polynomial algebras.NEWLINENEWLINENEWLINETwo short remarks concerning the application of the results to the integral and \(p\)-compact settings for the study of generalized homogeneous spaces conclude this note.