Vol. 19, No. 3, 1966

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ISSN: 0030-8730
An application of the Bott suspension map to the topology of EIV

Lawrence William Conlon

Vol. 19 (1966), No. 3, 411–428
Abstract

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
Milestones
Received: 31 August 1965
Published: 1 December 1966
Authors
Lawrence William Conlon