The Cohomology of Invariant Variational Bicomplexes

  • Ian M. Anderson
  • Juha Pohjanpelto


Let π: EM be a fiber bundle and let Γ be an infinitesimal Lie transformation group acting on E. We announce various new results concerning the cohomology of the Γ invariant variational bicomplex (Ω Γ *,* (J (E)),d H ,d V ) and the associated Γ 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.


Vector Field Regular Point Source Form Horizontal Connection Continuous Cohomology 
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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Ian M. Anderson
    • 1
  • Juha Pohjanpelto
    • 2
  1. 1.Department of MathematicsUtah State UniversityLoganUSA
  2. 2.Department of MathematicsOregon State UniversityCorvallisUSA

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