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 of ℤ and a finite group.
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Morel, F. (2004). On the Motivic π0 of the Sphere Spectrum. In: Greenlees, J.P.C. (eds) Axiomatic, Enriched and Motivic Homotopy Theory. NATO Science Series, vol 131. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0948-5_7
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DOI: https://doi.org/10.1007/978-94-007-0948-5_7
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