group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
By complex cohomology one usually means ordinary cohomology with complex number coefficients, denoted $H^\bullet\big(-, \mathbb{C}\big)$.
Hence, with the pertinent conditions on the domain space $X$ satisfied, its complex cohomology $H^\bullet\big(-, \mathbb{C}\big)$ is what is computed by the Cech cohomology or singular cohomology or sheaf cohomology of $X$ with coefficients in $\mathbb{C}$.
Last revised on December 5, 2020 at 15:50:55. See the history of this page for a list of all contributions to it.