A new infinite order formulation of variational sequences

R. Vitolo

Address. Department of Applied Mathematics ``E. De Giorgi", University of Lecce Via per Arnesano, 73100 Lecce, ITALY

E-mail: vitolo@ilenic.unile.it

Abstract. The theory of variational bicomplexes is a natural geometrical setting for the calculus of variations on a fibred manifold. It is a well--established theory although not spread out very much among theoretical and mathematical physicists. Here, we present a new approach to infinite order variational bicomplexes based upon the finite order approach due to Krupka. In this approach the information related to the order of jets is lost, but we have a considerable simplification both in the exposition and in the computations. We think that our infinite order approach could be easily applied in concrete situations, due to the conceptual simplicity of the scheme.

AMSclassification. 58A12, 58A20, 58E30, 58G05

Keywords. fibred manifold, jet space, infinite order jet space, variational bicomplex, variational sequence