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Revista Colombiana de Matemáticas

versión impresa ISSN 0034-7426

Rev.colomb.mat. v.39 n.1 Bogotá ene./jun. 2005


On the Hurewicz theorem for wedge sum of spheres


Fermin Dalmagro1 - Yamilet Quintana2*

1Escuela de Matemáticas. Facultad de Ciencias. Apartado Postal: 20513, Caracas 1020 A. Universidad Central de Venezuela. Avenida Los Ilustres, Los Chaguaramos.Caracas Venezuela


2Departamento de Matemáticas Puras y Aplicadas. Edificio Matemáticas y Sistemas (MYS). Universidad Simón Bolívar. Valle de Sartenejas, Baruta. Estado Miranda, Venezuela


Abstract. 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 ... Xn-1 C Xn = X is the CW decomposition of X, then the Hurewicz homomorphism ∏n+1 (Xn+1,Xn) → Hn+1 (Xn+1,Xn) 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) → Hn (X) is an isomorphism.

Keywords and phrases. Hurewicz homomorphism, CW-complexes, exact sequence, homotopic groups, homology groups.

2000 Mathematics Subject Classification. Primary: 55N10, 55N99, 55Q40. Secondary: 54F65.

Resumen. En este artículo damos una demostración alternativa de el teorema de Hurewicz cuando el espacio topológico X es CW-complejo. En realidad probamos que si X0 C X1 C ... Xn-1 C Xn = X es una descomposición CW de X, el homomorfismo de Hurewicz ∏n+1 (Xn+1,Xn) → Hn+1 (Xn+1,Xn) es un isomorfismo y usando un resultado de álgebra Homológica demostramos que si X es conexo, el homomorfismo de Hurewicz ∏n (X) → Hn (X) es un isomorfismo.


* Research partially supportes by DID-USB under Grant DI-CB-015-04.


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(Recibido en abril de 2005. Aceptado en julio de 2005)


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