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Sphere transitive structures and the triality automorphism

1970
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Pacific Journal of Mathematics
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1= 7 3 , λ(7 2 )=7 2 , λ(7 8 ) = 7 4 , λ(7 4 ) = 7i Henceforth we assume that the principal of triality holds and that the above choice of simple roots has been made. Since Spin (8) is simply connected, λ and K induce outer automorphisms of Spin (8); these in turn induce homeomorphisms of B Spin (8), which we continue to denote by λ and /c. In order to determine the cohomology of λ and fc, it will be convenient to use some cohomology classes introduced by Thomas [12]. Let p: B Spin (n) ->

doi:10.2140/pjm.1970.34.83
fatcat:gvvrknw4jrgdnbxuhkq5nujbli