Homology of iterated loop spaces of homogeneous spaces associated with exceptional Lie groups (Q538055)

The author studies \(H_*(\Omega^n(G/H);\mathbb F_2)\) \((n=2,3)\) for homogeneous spaces \(G/H\) with \(G\) and \(H\) exceptional Lie groups. The method is to calculate two spectral sequences: one is the Serre spectral sequence for the fibration \(\Omega^{n}G \to \Omega^{n}(G/H) \to \Omega^{n-1}H\), and the other is the Eilenberg-Moore spectral sequence associated with the path loop fibration \(\Omega^{n}(G/H) \to P(\Omega^{n-1}(G/H))\to \Omega^{n-1}(G/H)\).