منابع مشابه
The Adams Conjecture
THIS paper contains a demonstration of the Adams conjecture [l] for real vector bundles. Unlike an old attempt of mine [12], which has recently been completed by Friedlander [S], and the proof of Sullivan [1.5], no use is made of the etale topology of algebraic varieties. The proof uses only standard techniques of algebraic topology together with some basic results on the representation rings o...
متن کاملThe Adams Conjecture, after Edgar Brown
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 \...
متن کاملTwo Proofs of the Stable Adams Conjecture
(P) where / is the complex /-homomorphism and , y denotes localization at p. Both J and ** are infinite loop maps, and it is natural to ask whether this result is infinitely deloopable; that is, whether J<ff = / as infinite loop maps. This is the Stable Adams Conjecture. We announce here two independent proofs of this conjecture. Details will appear in [2] and [6]. METHOD 1. Our proof is based ...
متن کاملQuillen’s Work on the Adams Conjecture
In the 1960’s and 1970’s, the Adams Conjecture figured prominently both in homotopy theory and in geometric topology. Quillen sketched one way to attack the conjecture and then proved it with an entirely different line of argument. Both of his approaches led to spectacular and beautiful new mathematics. 1. Background on the Adams Conjecture For a finite CW -complex X, let KO(X) be the Grothendi...
متن کاملGenetics of Homotopy Theory and the Adams Conjecture
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ژورنال
عنوان ژورنال: Topology
سال: 1971
ISSN: 0040-9383
DOI: 10.1016/0040-9383(71)90018-8