Homology of the double and the triple loop spaces¶of E6, E7, and E8

Abstract

We study the mod p homology of the double and the triple loop spaces of exceptional Lie groups E 6, E 7, and E 8 through the Eilenberg–Moore spectral sequence and the Serre spectral sequence using homology operations. The Bockstein actions on them are also determined. As a result, the Eilenberg–Moore spectral sequences of the path loop fibrations converging to H *(Ω2 G;? p ) and H *(Ω3 G;? p ) collapse at the E 2-term for any compact simple Lie group G.