nLab
complex cohomology

Contents

Context

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Contents

Idea

By complex cohomology one usually means ordinary cohomology with complex number coefficients, denoted H (,)H^\bullet\big(-, \mathbb{C}\big).

Hence, with the pertinent conditions on the domain space XX satisfied, its complex cohomology H (,)H^\bullet\big(-, \mathbb{C}\big) is what is computed by the Cech cohomology or singular cohomology or sheaf cohomology of XX with coefficients in \mathbb{C}.

Properties

Last revised on December 5, 2020 at 10:50:55. See the history of this page for a list of all contributions to it.