Vol. 19, No. 3, 1966

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An application of the Bott suspension map to the topology of EIV

Lawrence William Conlon

Vol. 19 (1966), No. 3, 411–428

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.

Mathematical Subject Classification
Primary: 55.45
Secondary: 57.45
Received: 31 August 1965
Published: 1 December 1966
Lawrence William Conlon