For an (n−1)-connected space X (n ≥ 2), the Hurewicz map h_n: π_n(X) → H_n(X; Z) is an isomorphism. The n = 1 case gives π₁(X)^(ab) ≅ H₁(X; Z) (Poincaré 1895). Key tool connecting homotopy and homology. Example: S^n is (n−1)-connected…
For an (n−1)-connected space X (n ≥ 2), the Hurewicz map h_n: π_n(X) → H_n(X; Z) is an isomorphism. The n = 1 case gives π₁(X)^(ab) ≅ H₁(X; Z) (Poincaré 1895). Key tool connecting homotopy and homology. Example: S^n is (n−1)-connected…