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5-th Conference on Geometry and Topology of Manifolds
April 27 - May 3, 2003

Krynica, Poland

Organizers
Institute of Mathematics of the Technical University of Lodz; Institute of Mathematics of the Jagiellonian University, Cracow; Faculty of Applied Mathematics of the University Mining and Matallurgy, Cracow

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Transitive Lie algebroids: spectral sequences and signature
by
Alexandr Mishchenko
Moscow State University, Moscow, Russia
Coauthors: Jan Kubarski

We prove that for any transitive unimodular invariantly oriented Lie algebroid L on a compact, oriented and connected manifold with isotropy Lie algebra \mathfrakg and trivial monodromy the cohomology algebra is the Poincaré algebra with trivial signature. In particular, the examples of such algebroids are when M is simply connected or when \operatornameAutG=\operatornameIntG, for simply connected Lie group G with the Lie algebra \mathfrakg, or when the adjoint Lie algebra bundle \pmbg induces trivial homology bundle H * (\pmbg) in the category of flat bundles.

Date received: April 26, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cakm-19.