Freudenthal suspension theorem

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This fact is related to: homotopy groups

Statement

Let X be a (n-1)-connected space having a nondegenerate basepoint x_0. Then the suspension homomorphism from \pi_q(X) \to \pi_{q+1}(\Sigma X) is an isomorphism for q \le 2n - 2 and is surjective for q = 2n - 1.