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Proyecciones (Antofagasta)

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Abstract

PEREIRA, M. S.  and  DOS SANTOS, N. M.. ON THE COHOMOLOGY OF FOLIATED BUNDLES. Proyecciones (Antofagasta) [online]. 2002, vol.21, n.2, pp.175-197. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172002000200005.

We prove a de Rham-like theorem for foliated bundles F ! (M; F )¼ ! B showing that the cohomology H¤( F ) is isomorphicto the equivariant cohomology H¡ ³ eB; C1 (F); ¡ = ¼1 (B)and eB the universal covering of B. When B is an Eilenberg-Mac Lane space K (¡; 1) the cohomology H¤ ( F ) is the cohomology of the ¡-module C1 (F). This gives algebraic models for H¤ ( F ) and geometrial models for the cohomology of the ¡-module C1 (F). 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

Keywords : foliated bundles; foliated cohomology; equivariant cohomology; cohomology of groups.

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