group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
By real cohomology one usually means ordinary cohomology with real number coefficients, denoted .
Hence, with the pertinent conditions on the domain space satisfied, its real cohomology is what is computed by the Cech cohomology or singular cohomology or sheaf cohomology of with coefficients in .
In particuar, for a smooth manifold, the de Rham theorem says that real cohomology of is also computed by the de Rham cohomology of
More generally, for a smooth manifold with smooth action of a connected compact Lie group, the equivariant de Rham theorem says that the real cohomology of the homotopy quotient (e.g. Borel construction) of is computed by the Cartan model for equivariant de Rham cohomology on .
cohomology | Borel-equivariant cohomology |
---|---|
real ordinary cohomology | real equivariant ordinary cohomology |
de Rham cohomology | equivariant de Rham cohomology |
Last revised on December 5, 2020 at 15:50:25. See the history of this page for a list of all contributions to it.