Basic forms and orbit spaces: A diffeological approach

Yael Karshon, Jordan Watts

Research output: Contribution to journalArticlepeer-review


If a Lie group acts on a manifold freely and properly, pulling back by the quotient map gives an isomorphism between the differential forms on the quotient manifold and the basic differential forms upstairs. We show that this result remains true for actions that are not necessarily free nor proper, as long as the identity component acts properly, where on the quotient space we take differential forms in the diffeological sense.

Original languageEnglish
Article number026
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
StatePublished - 8 Mar 2016
Externally publishedYes


  • Basic differential forms
  • Diffeology
  • Lie group actions
  • Orbit space


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