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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.21 no.2 Antofagasta Aug. 2002

http://dx.doi.org/10.4067/S0716-09172002000200005 

Proyecciones
Vol. 21, N o 2, pp. 175-197, August 2002.
Universidad Católica del Norte
Antofagasta - Chile

ON THE COHOMOLOGY OF FOLIATED BUNDLES ¤

M. S. PEREIRA
N. M. DOS SANTOS
Universidade Federal Fluminense - Brasil

Abstract

We prove a de Rham-like theorem for foliated bundles showing that the cohomology H *( F ) is isomorphicto the equivariant cohomology and eB the universal covering of B. When B is an Eilenberg-Mac Lane space the cohomology H *( F ) is the cohomology of the . This gives algebraic models for H *( F ) and geometrial models for the cohomology of the Using this isomorphism and a theorem of J. Palis and J.C. Yoccoz on the triviality of centralizers of diffeomorphisms, [14] and [15] we show that H *(F ) is infinite dimensional for a large class of foliated bundles. Using this isomorphism R. u. Luz computed in [9] the cohomology of the foliated bunddles suspensions of actions of Z P by afine transformations of Tq.

AMS (MOS) Subj class
: 57R30

Key Words: foliated bundles, foliated cohomology, equivariant cohomology, cohomology of groups.

¤This paper is in final form and no version of it will be submited for publication elsewhere. Partly supported by the CNPq/MCT-PR/Brasil.

References

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Received : November, 2001.

Maria do Socorro Pereira

And

Nathan Moreira dos Santos
Instituto de Matemática
Universidade Federal Fluminense
CEP 24020-005
Niteroi Brazil
e-mail : nathanmoreira@ig.com.br

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