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On the Motivic π0 of the Sphere Spectrum

  • Fabien Morel
Part of the NATO Science Series book series (NAII, volume 131)

Abstract

Let d ≥ 1 and X a pointed topological space. We denote as usual by π d (X) the d-th homotopy group of X. One of the starting point in homotopy theory is the following result: Theorem 1.1.1. Let n > 0 be any integer. 1) If d < n then π d (S n ) = 0; 2) If d = n then π n (S n ) = ℤ ; 2) (Serre) If d > n then π d (S N ) is a finite group unless n is even and d = 2n - 1 in which case it a direct sum ofand a finite group.

Keywords

Full Subcategory HOMOTOPY Theory Triangulate Category Witt Ring Adams Spectral Sequence 
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Copyright information

© Springer Science+Business Media Dordrecht 2004

Authors and Affiliations

  • Fabien Morel
    • 1
  1. 1.Institut de MathématiquesUniversité Paris 7JussieuParisFrance

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