Homology of iterated loop spaces of homogeneous spaces associated with exceptional Lie groups

Abstract

We study the mod 2 homology of the double and triple loop spaces of homogeneous spaces associated with exceptional Lie groups. The main computational tools are the Serre spectral sequence for fibrations Ω n + 1 G → Ω n + 1 ( G / H ) → Ω n H for n = 1 , 2 , and the Eilenberg–Moore spectral sequence associated with related fiber squares, which both converge to the same destination space H ∗ ( Ω n ( G / H ) ; F 2 ) . We also develop the generalized Bockstein lemma to determine the higher Bockstein actions.