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On the Hurewicz theorem for wedge sum of spheres
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Hurewicz homomorphism, CW-complexes, Exact sequence. Homotopic groups, Homology groups, 2000 Mathematics Subject Classification, Primary: 55N10, 55N99, 55Q40. Secondary: 54F65. (en)Descargas
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 Xo ⊆ X1 ⊆ … Xn-i ⊆ Xn = X is the CW decomposition of X, then the Hurewicz homomorphism ∏n+1 (Xn-I, Xn) → Hn+1 (Xn-I, 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.
Sea p > 2 un primo y Λ = ℤP[[X]] el anillo de series de potencias con coeficientes enteros p-adicos. El grupo lineal de matrices especial SL(2, Λ) es equipado con varias proyecciones naturales. En particular, πx : SL(2, Λ) → SL(2, ℤP) es la proyección natural que envia X ↦ 0. Suponga que G es un subgrupo de SL(2, Λ) tal que la proyección H = πx (G) es conocida. En este artículo se establecen diferentes criterios que garantizan que el subgrupo G de SL(2, Λ) es “tan grande como es posible”; esto es, G es la imagen inversa total de H. Criterios de esta naturaleza tienen importantes aplicaciones a la teoría de representaciones de Galois.
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