Resumen de Theorémes de Zilber-Eilemberg et de Brown en homologie ℓ₁

Abdesselam Bouarich

• 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 ℓ₁-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 ℓ₁-singular homology. In last section, we prove an analogous of Brown theorem in real ℓ₁-singular homology. As consequence of this theorem we show that the real ℓ₁-singular homology depends only on the fundamental group and we establish some exact sequences.