International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 1, Pages 39-47
doi:10.1155/S0161171202012097

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

Abstract

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.