Annals of Global Analysis and Geometry

, Volume 7, Issue 3, pp 163–169 | Cite as

A cohomology for vector valued differential forms

  • Peter W. Michor
  • Hubert Schicketanz
Article
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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.

Keywords

Group Theory Direct Product Related Result Differential Form Algebra Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© VEB Deutscher Verlag der Wissenschaften 1989

Authors and Affiliations

  • Peter W. Michor
    • 1
  • Hubert Schicketanz
    • 2
  1. 1.Institut für MathematikUniversität WienWein
  2. 2.Institut de MathématiqueUniversité de LiègeLeège

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