Abstract

DALMAGRO, Fermin  and  QUINTANA, Yamilet. On the Hurewicz theorem for wedge sum of spheres. Rev.colomb.mat. [online]. 2005, vol.39, n.1, pp. 21-35. ISSN 0034-7426.

This paper we provides an alternative proof of Hurewicz theorem when the topological space X is a CW-complex. Indeed, we show that if X₀ C X₁ C ... X_{n-1 C} X_n = X is the CW decomposition of X, then the Hurewicz homomorphism ∏_n+1 (X_n+1,X_n) → H_n+1 (X_n+1,X_n) is an isomorphism, and together with a result from Homological Algebra we prove that if X is (n-1)-connected, the Hurewicz homomorphism ∏_n (X) → H_n (X) is an isomorphism.

Keywords : Hurewicz homomorphism; CW-complexes; exact sequence; homotopic groups; homology groups.