Basic Forms and Orbit Spaces: a Diffeological Approach

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2016
• Main Authors: Karshon, Y., Watts, J.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2016
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147723
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Basic Forms and Orbit Spaces: a Diffeological Approach / Y. Karshon, J. Watts // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 30 назв. — англ.

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,...