THE VARIATIONAL BICOMPLEX

By ANDREW WILSON

A IN?NITE JET BUNDLES B VECTOR FIELDS AND GENERALIZED VECTOR FIELDS C DI?ERENTIAL FORMS AND THE VARIATIONAL BICOMPLEX D PROLONGATIONS OF GENERALIZED VECTOR FIELDS CHAPTER TWO EULER OPERATORS A TOTAL DI?ERENTIAL OPERATORS B EULER OPERATORS C SOME GEOMETRIC VARIATIONAL PROBLEMS CHAPTER THREE FUNCTIONAL FORMS AND COCHAIN MAPS A FUNCTIONAL FORMS B COCHAIN MAPS ON THE VARIATIONAL BICOMPLEX C A LIE DERIVATIVE FORMULA FOR FUNCTIONAL FORMS CHAPTER FOUR LOCAL PROPERTIES OF THE VARIATIONAL BICOMPLEX A LOCAL EXACTNESS AND THE HOMOTOPY OPERATORS FOR THE VARIATIONAL BICOMPLEX B MINIMAL WEIGHT FORMS C THE JACOBIAN SUBCOMPLEX CHAPTER FIVE GLOBAL PROPERTIES OF THE VARIATIONAL BICOMPLEX A HORIZONTAL COHOMOLOGY OF THE VARIATIONAL BICOMPLEX B VERTICAL COHOMOLOGY OF THE VARIATIONAL BICOMPLEX C GENERALIZED POINCAR´E -CARTAN FORMS AND NATURAL DI?ERENTIAL OPERATORS ON THE VARIATIONAL BICOMPLEX D INVARIANT HORIZONTAL HOMOTOPY OPERATORS ON MANIFOLDS WITH SYMMETRIC CONNECTIONS CHAPTER SIX EQUIVARIANT COHOMOLOGY OF THE VARIATIONAL BICOMPLEX‡ A GELFAND-FUKS COHOMOLOGY B THE VARIATIONAL BICOMPLEX FOR NATURAL RIEMANNIAN STRUCTURES CHAPTER SEVEN THE VARIATIONAL BICOMPLEX FOR DIFFERENTIAL EQUATIONS‡ A PRELIMINARIES B THE TWO LINE THEOREM AND ITS GENERALIZATION C EXAMPLES D THE INVERSE PROBLEM TO THE CALCULUS OF VARIATIONS REFERENCES