nLab complex cohomology

Idea

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 $\mathbb{C}$.

Properties

• de Rham theorem

• PL de Rham theorem

Related concepts

• Dolbeault cohomology

• complex vector space

• integral cohomology, rational cohomology, real cohomology