Affiliation:
1. Departamento de Economía Financiera y Contabilidad I, Facultad de Ciencias Económicas y Empresariales, UCM Campus de Somosaguas, 28223-Pozuelo de Alarcón, Spain
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 [Formula: see text] acts on E, we can define the local [Formula: see text]-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 [Formula: see text]-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.
Publisher
World Scientific Pub Co Pte Lt
Subject
Physics and Astronomy (miscellaneous)
Reference15 articles.
1. The cohomology of invariant variational bicomplexes
2. I. Anderson, Differential Geometry and Applications (Brno, 1995) (Masaryk Univ., Brno, 1996) pp. 427–448.
3. R. Bott, Notes on Gel'fand Fuks Cohomology and Characteristic Classes 3 (Birkhäuser Boston, 1995) pp. 288–356.
4. The geometry of the bundle of connections
5. Equivariant characteristic forms on the bundle of connections
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献