The \(\text{mod }3\) homology of the space of loops on the exceptional Lie groups and the adjoint action
The title of this paper accurately describes its contents -- the determination of the homology of the loop space \(\Omega G\) at the prime 3, where \(G\) is one of the five exceptional Lie groups, together with the induced adjoint action. the results are motivated by R. Bott's theorem that \(H*(\Omega G, \mathbb{Z}/p)\) is a finitely-generated bicommutative Hopf algebra, generated in even degrees, and his determination of this algebra when \(G\) belongs to one of the families of classical groups. The main additional ingredient needed is the (co)homology of the groups concerned, which to a large extent is labeled by the exponents of the group. We must also remember that in most cases the prime 3 also divides the order of the Weyl group.
cohomology of specific Lie groups and spaces
scientific article; zbMATH DE number 1189511