Homogeneous variational complexes and bicomplexes

Details Homogeneous variational complexes and bicomplexes Homogeneous variational complexes and bicomplexes

2005-12-16

arxiv.org/abs/math/0512383v1

Mathematics

Differential Geometry

21 pages

Scientific paper

We present a family of complexes playing the same role, for homogeneous variational problems, that the horizontal parts of the variational bicomplex play for variational problems on a fibred manifold. We show that, modulo certain pullbacks, each of these complexes (apart from the first one) is globally exact. All the complexes may be embedded in bicomplexes, and we show that, again modulo pullbacks, the latter are locally exact. The edge sequence is an important part of such a bicomplex, and may be used for the study of homogeneous variational problems.

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