  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.

Geometric Topology;Differential Geometry;Symplectic Geometry