Theorémes de Zilber-Eilemberg et de Brown en homologie ℓ₁
-
Bouarich, Abdesselam [1]
-
[1] Cadi Ayyad University
Cadi Ayyad University
Marrakech-Medina, Marruecos
-
- Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 23, Nº. 2, 2004, págs. 151-186
- Idioma: español
- DOI: 10.4067/S0716-09172004000200007
- Enlaces
-
Resumen
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.
-
Referencias bibliográficas
- Citas [1] A. Bouarich, Suites exactes en cohomologie bornée réelle des groupes discrets, C.R.A.S. Paris, t. 320, Série 1, p. 1355-1359 (1995).
- [2] A. Bouarich, Exactutide a gauche du foncteur Hb ∗(−, R) de cohomologie bornée réelle, Annales de la Faculté de Toulouse, Vol. X, No. 2,...
- [3] E. Brown, Twisted tensor product, Annals of Math. Vol. 69, No. 1, p. 223-246, (1959).
- [4] S. Eilenberg and S. Maclane, Acyclic Models, Amer. Jour. Math, Vol. 75, 189-199 (1953).
- [5] S. Eilenberg and J.A. Zilber, On product of complexes, Amer. Jour. Math, Vol. 75, 200-204, (1953).
- [6] R. Godment, Théorie des faisceaux, Herman Paris (1953).
- [7] P. Greenleaf, Invariants means on topological groups, Van Nostrand Math. Studies, (1969).
- [8] M. Gromov, Volume and Bounded Cohomology, IHES, (1981).
- [9] A. Grothendeik, Produits tensoriels topologiques et espaces nucléaires, Mem. of American Soc. Vol. 16, (1966).
- [10] V. Ivanov, Foundation of the theory of bounded cohomoloy, J. of Soviet Math. 37, 1090-1115, (1987).
- [11] S. Maclane, Categories for Working mathematician, Springer-Verlag.
- [12] Matsumoto-Morita, Bounded cohomology of certain groups of homeomorphisms, Proc. of the AMS, Vol. 94, No. 1, p. 539-544, (1986)
- [13] J. McCleary, User’s guide to spectral sequences, Publish or Perish, Inc (U.S.A), (1984).
- [14] K. Yosida, Functional Analysis, Springer-Verlag, Berlin, (1966).
- [15] G. Whithead, Elements of homotopy theory, Springer-Verlag, Berlin, (1978).
