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LOCAL COHOMOLOGY AND THE VARIATIONAL BICOMPLEX.

Authors :
PÉREZ, ROBERTO FERREIRO
Source :
International Journal of Geometric Methods in Modern Physics. Jun2008, Vol. 5 Issue 4, p587-604. 18p.
Publication Year :
2008

Abstract

The differential forms on the jet bundle J∞E of a bundle E → M over a compact n-manifold M of degree greater than n determine differential forms on the space Γ(E) of sections of E. The forms obtained in this way are called local forms on Γ(E), and its cohomology is called the local cohomology of Γ(E). More generally, if a group $\mathcal{G}$ acts on E, we can define the local $\mathcal{G}$-invariant cohomology. The local cohomology is computed in terms of the cohomology of the jet bundle by means of the variational bicomplex theory. A similar result is obtained for the local $\mathcal{G}$-invariant cohomology. Using these results and the techniques for the computation of the cohomology of invariant variational bicomplexes in terms of relative Gelfand–Fuchs cohomology introduced in [4], we construct non trivial local cohomology classes in the important cases of Riemannian metrics with the action of diffeomorphisms, and connections on a principal bundle with the action of automorphisms. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
02198878
Volume :
5
Issue :
4
Database :
Academic Search Index
Journal :
International Journal of Geometric Methods in Modern Physics
Publication Type :
Academic Journal
Accession number :
32853130