ON THE COHOMOLOGY OF FOLIATED BUNDLES
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...
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Universidad Católica del Norte, Departamento de Matemáticas
2002
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oai:scielo:S0716-091720020002000052002-10-31ON THE COHOMOLOGY OF FOLIATED BUNDLESPEREIRA,M. S.DOS SANTOS,N. M. foliated bundles foliated cohomology equivariant cohomology cohomology of groups 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 T Q. AMS (MOS) Subj class: 57R30info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.21 n.2 20022002-08-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172002000200005en10.4067/S0716-09172002000200005 |
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Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
foliated bundles foliated cohomology equivariant cohomology cohomology of groups |
| spellingShingle |
foliated bundles foliated cohomology equivariant cohomology cohomology of groups PEREIRA,M. S. DOS SANTOS,N. M. ON THE COHOMOLOGY OF FOLIATED BUNDLES |
| description |
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 T Q. AMS (MOS) Subj class: 57R30 |
| author |
PEREIRA,M. S. DOS SANTOS,N. M. |
| author_facet |
PEREIRA,M. S. DOS SANTOS,N. M. |
| author_sort |
PEREIRA,M. S. |
| title |
ON THE COHOMOLOGY OF FOLIATED BUNDLES |
| title_short |
ON THE COHOMOLOGY OF FOLIATED BUNDLES |
| title_full |
ON THE COHOMOLOGY OF FOLIATED BUNDLES |
| title_fullStr |
ON THE COHOMOLOGY OF FOLIATED BUNDLES |
| title_full_unstemmed |
ON THE COHOMOLOGY OF FOLIATED BUNDLES |
| title_sort |
on the cohomology of foliated bundles |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2002 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172002000200005 |
| work_keys_str_mv |
AT pereirams onthecohomologyoffoliatedbundles AT dossantosnm onthecohomologyoffoliatedbundles |
| _version_ |
1718439727191818240 |