The Adams Conjecture, after Edgar Brown
نویسنده
چکیده
Let X be a finite CW-complex. Denote by Sph(X) the abelian group of stable fibre-homotopy classes of spherical fibrations on X. Let F (n) be the monoid of self-homotopy-equivalences of S and let F := colimn→∞ F (n). The classifying space BF represents Sph(X), i.e. Sph(X) ∼= [X;BF ]. For any vector bundle ξ on X, let J(ξ) ∈ Sph(X) be the stable fibre homotopy class of the spherical fibration ξ \ 0 → X (cut out the zero-section). This construction defines a homomorphism J : KO(X) → Sph(X).
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