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Adams operations on KO(X) ⊕ KSp (X) Allard, Jacques

Abstract

Let KO(X) be the real and KSP(X) be the quaternionic K-theory of a finite CW-complex X . The tensor product and the exterior powers of vector bundles induce on L(X) = KO(X) ⊕ KSP(X) the structure of Z₂ -graded λ-ring. In this thesis it is shown, that the Adams operations Ѱk : L(X) → L(X) , k = l, 2, 3,..., which are associated to this λ-ring, are ring homomorphisms and satisfy the composition law Ѱk ₀ Ѱℓ = Ѱℓk = Ѱℓ ₀ Ѱk , k, ℓ = 1, 2, 3,... Finally, the ring L(X) together with its Ѱ-operations is explicitely determined for the quaternionic and complex projective spaces.

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