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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.23 n.2 Antofagasta ago. 2004

http://dx.doi.org/10.4067/S0716-09172004000200007 

 

Proyecciones
Vol. 23, No 2, pp. 151-186, August 2004.
Universidad Católica del Norte
Antofagasta - Chile

THÉORÈMES DE ZILBER-EILEMBERG ET DE BROWN EN HOMOLOGIE

 

ABDESSELAM BOUARICH

Université Cadi Ayyad, Maroc

Received : December 2003. Accepted : July 2004

correspondencia a:


Abstract

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

AMS Classification : 46M15, 46A30, 46A32, 14F99.


References

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[2] A. Bouarich, Exactutide à gauche du foncteur H¤b (-,R) de cohomologie bornée réelle, Annales de la Faculté de Toulouse, Vol. X, No. 2, p. 255-270, (2001).        [ Links ]

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[10] V. Ivanov, Foundation of the theory of bounded cohomoloy, J. of Soviet Math. 37, 1090-1115, (1987).        [ Links ]

[11] S. Maclane, Categories for Working mathematician, Springer-Verlag.        [ Links ]

[12] Matsumoto-Morita, Bounded cohomology of certain groups of homeomorphisms, Proc. of the AMS, Vol. 94, No. 1, p. 539-544, (1986)        [ Links ]

[13] J. McCleary, User's giide to spectral sequences, Publish or Perish, Inc (U.S.A), (1984).        [ Links ]

[14] K. Yosida, Functional Analysis, Springer-Verlag, Berlin, (1966).        [ Links ]

[15] G. Whithead, Elements of homotopy theory, Springer-Verlag, Berlin, (1978).        [ Links ]

Abdesselam Bouarich
Université Cadi Ayyad
Faculté des Sciences et Téchniques
BP. 523, Beni Mellal
Maroc
e-mail : bouarich1@yahoo.fr

 

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