Mark V. Losik
A Note on the Cohomology of the Complex of G-Invariant Forms on G-Manifolds
Preprint series: ESI preprints

MSC:

57R91 Equivariant algebraic topology of manifolds

Abstract: The cohomology of a certain class of $G$-manifolds, which
are locally trivial fiber bundles over the orbit space, is
considered. For a reductive Lie group $G$ the conditions are indicated
which allows to construct a convenient cochain complex with the cohomology
isomorphic to the cohomology of the complex of $G$-invariant forms on $M.$
In particular, these conditions are satisfied for a compact Lie group $G.$

Keywords: $G$-manifolds, fiber bundle, cohomology, spectral sequence