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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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Geometric interpretation of cohomology classes and application to the case of smooth manifolds
by
Sarah Hansoul
FNRS fellowship, University of Liège
Coauthors: Pierre B. A. Lecomte

In this lecture, we explain how to use cohomology classes to define a representation of a Lie algebra on the space of polynomial maps from an affine space to a vector space.

We apply this construction to endow, given an affine representation of a Lie algebra L, a representation of L on polynomial maps in a natural way.

We then compute some Chevalley cohomology space of the Lie algebra of vector fields on a manifold, valued in polynomial maps on affine connections on this manifold.

Date received: April 25, 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-15.