On the Cohomology of Invariant Variational Bicomplexes

Let Pi = E rarr M be a fiber bundle and let Gamma be an infinitesimal Lie transformation group acting onE. We announce various new results concerning the cohomology of the Gamma invariant variational bicomplex (OHgr Gamma *,* (Jinfin(E)), dH, dV) and the associated Gamma invariant Euler-Lagrange complex. As one application of our general theory, we completely solve the local invariant inverse problem of the calculus of variations for finite-dimensional infinitesimal Lie transformation groups