Mod p homology of F4–gauge groups over S4

We study the mod p homology of the gauge group G k ( F 4 ) associated with a principal F 4 bundle by computing the Serre spectral sequence for the fibration Ω 0 4 ( F 4 ) → G k ( F 4 ) → F 4 . The main result is that the Serre spectral sequence collapses at the E 2 -term except for p = 2 , 13 .