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On a bicomplex induced by the variational sequence. (English) Zbl 1322.58013

In this paper, the authors consider variational sequences on fibered manifolds over one-dimensional base manifolds and within the framework of the variational sequence theory. They introduce analogues of the horizontal and vertical derivatives, used in the bicomplex theory. They construct a variational bicomplex by means of an infinite canonical construction from the variational sequence theory; the construction involves an extension of the sequence morphisms to the bicomplex classes. Then, they study the relationship between the morphisms and classes entering the variational sequence and the associated finite-order bicomplex.

MSC:

58E30 Variational principles in infinite-dimensional spaces
58A10 Differential forms in global analysis
58A20 Jets in global analysis
70G75 Variational methods for problems in mechanics
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