THÉORÈMES DE ZILBER-EILEMBERG ET DE BROWN EN HOMOLOGIE l1

Notion of acyclic models are introduced in Eleinberg-Maclane [4]. In [5] and [3], this theory is used as auxiliary tools to solve extension problems of morphisms of chains complexes and homotopy between those morphisms. So in the first section of this work, we will adapt the notion of acyclic models...

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Autor principal: BOUARICH,ABDESSELAM
Lenguaje:French
Publicado: Universidad Católica del Norte, Departamento de Matemáticas 2004
Acceso en línea:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172004000200007
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spelling oai:scielo:S0716-091720040002000072004-09-29THÉORÈMES DE ZILBER-EILEMBERG ET DE BROWN EN HOMOLOGIE l1BOUARICH,ABDESSELAMNotion of acyclic models are introduced in Eleinberg-Maclane [4]. In [5] and [3], this theory is used as auxiliary tools to solve extension problems of morphisms of chains complexes and homotopy between those morphisms. So in the first section of this work, we will adapt the notion of acyclic models in the category of Banach chain differential complexes Ch¤(Ban). In the second section, we recall the functor of real `1- singular homology (cf. [8]) on which we apply theorems proved in the first section. In particular, we prove an analogous of Zilber-Eilenberg theorem [5] in real `1-singular homology. In last section, we prove an analogous of Brown theorem in real `1-singular homology. As consequence of this theorem we show that the real `1-singular homology depends only on the fundamental group and we establish some exactinfo:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.23 n.2 20042004-08-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172004000200007fr10.4067/S0716-09172004000200007
institution Scielo Chile
collection Scielo Chile
language French
description Notion of acyclic models are introduced in Eleinberg-Maclane [4]. In [5] and [3], this theory is used as auxiliary tools to solve extension problems of morphisms of chains complexes and homotopy between those morphisms. So in the first section of this work, we will adapt the notion of acyclic models in the category of Banach chain differential complexes Ch¤(Ban). In the second section, we recall the functor of real `1- singular homology (cf. [8]) on which we apply theorems proved in the first section. In particular, we prove an analogous of Zilber-Eilenberg theorem [5] in real `1-singular homology. In last section, we prove an analogous of Brown theorem in real `1-singular homology. As consequence of this theorem we show that the real `1-singular homology depends only on the fundamental group and we establish some exact
author BOUARICH,ABDESSELAM
spellingShingle BOUARICH,ABDESSELAM
THÉORÈMES DE ZILBER-EILEMBERG ET DE BROWN EN HOMOLOGIE l1
author_facet BOUARICH,ABDESSELAM
author_sort BOUARICH,ABDESSELAM
title THÉORÈMES DE ZILBER-EILEMBERG ET DE BROWN EN HOMOLOGIE l1
title_short THÉORÈMES DE ZILBER-EILEMBERG ET DE BROWN EN HOMOLOGIE l1
title_full THÉORÈMES DE ZILBER-EILEMBERG ET DE BROWN EN HOMOLOGIE l1
title_fullStr THÉORÈMES DE ZILBER-EILEMBERG ET DE BROWN EN HOMOLOGIE l1
title_full_unstemmed THÉORÈMES DE ZILBER-EILEMBERG ET DE BROWN EN HOMOLOGIE l1
title_sort théorèmes de zilber-eilemberg et de brown en homologie l1
publisher Universidad Católica del Norte, Departamento de Matemáticas
publishDate 2004
url http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172004000200007
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