Natural operations on differential forms

  title={Natural operations on differential forms},
  author={Jos'e Navarro and Juan Blanco Sancho},
  journal={arXiv: Differential Geometry},
We prove that the only natural operations between differential forms are those obtained using linear combinations, the exterior product and the exterior differential. Our result generalises work by Palais and Freed-Hopkins. As an application, we also deduce a theorem, originally due to Kolar, that determines those natural differential forms that can be associated to a connection on a principal bundle. 
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  • Global Anal. Geom
  • 1988
Foundations of differential geometry, Vol II, Wiley-Interscience Publishers, New York
  • 1969