Consider the compact
simply connected symmetric pair (E6,F4). By a slight abuse of the notation of E.
Cartan, the corresponding symmetric space is denoted by EIV . Let W be the Cayley
projective plane. The Bott suspension map E : Σ(W) → EIV (where Σ
denotes the nonreduced suspension) is defined by means of the set of minimal
geodesic segments joining the two nontrivial points of the “center” of EIV . In
this paper a map q : S25→ Σ(W) is constructed and E is extended to a
homeomorphism of Σ(W) ∪qe26 onto EIV . Among other things, this gives canonical
isomorphisms πj(EIV ) ≈ πj(Σ(W)),0 ≦ j ≦ 24. These groups are explicitly
determined.
