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

Gennadi Sardanashvily

 Department of Theoretical Physics, Moscow State University, Moscow 117234, Russia
Received 19 February 2001; Revised 18 September 2001

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.