A cohomology for vector valued differential forms |
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Authors: | Peter W Michor Hubert Schicketanz |
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Institution: | (1) Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Wein;(2) Institut de Mathématique, Université de Liège, Avenue des Tilleuls, 5, B-4000 Leège |
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Abstract: | A rather simple natural outer derivation of the graded Lie algebra of all vector valued differential forms with the Frölicher-Nijenhuis bracket turns out to be a differential and gives rise to a cohomology of the manifold, which is functorial under local diffeomorphisms. This cohomology is determined as the direct product of the de Rham cohomology space and the graded Lie algebra of traceless vector valued differential forms, equipped with a new natural differential concomitant as graded Lie bracket. We find two graded Lie algebra structures on the space of differential forms. Some consequences and related results are also discussed. |
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