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Homogeneous variational complexes and bicomplexes. (English) Zbl 1168.58006
A family of complexes is described playing the same rôle for homogeneous variational problems that the horizontal parts of the variational bicomplex play for variational problems on a fibered manifold. It is shown that – except one of them – these complexes are globally exact modulo certain pullbacks. All the complexes may be embedded in bicomplexes, and it is shown that, again modulo pullbacks, the latter are locally exact. Finally, a detailed discussion is provided on the edge sequence – an important part of such a bicomplex, which proves to be useful in the study of homogeneous variational problems.

MSC:
58E99 Variational problems in infinite-dimensional spaces
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