##
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