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International Journal of Mathematics and Mathematical Sciences
Volume 30, Issue 1, Pages 39-47

Cohomology of the variational complex in the class of exterior forms of finite jet order

Department of Theoretical Physics, Moscow State University, Moscow 117234, Russia

Received 19 February 2001; Revised 18 September 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We obtain the cohomology of the variational complex on the infinite-order jet space of a smooth fiber bundle in the class of exterior forms of finite jet order. In particular, this provides a solution of the global inverse problem of the calculus of variations of finite order on fiber bundles.