An application of the Bott suspension map to the topology ofEIV

Consider the compact simply connected symmetric pair (E 6 , Ft). 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:(W)-+EIV (where 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: S 25 - {W) is constructed and E is extended to a homeomorphism of (W) U q e 26 onto EIV. Among other things, this gives canonical isomorphisms j(EIV) j((W)), 0 ^ j ^ 24. These groups are explicitly determined.