cohomologi
Cohomologi, or cohomology in English, is a mathematical tool in algebraic topology that assigns to a topological space a sequence of abelian groups (or modules) H^n(X; A) that encode global properties. It is conceptually dual to homology and is especially useful for studying maps, geometry, and the ways spaces can be glued together.
There are several concrete constructions of cohomology theories. Singular cohomology uses cochains on all singular simplices
Definition and basic structure: For a space X and coefficient group A, one forms a cochain complex
Key properties and theorems: Cohomology is functorial, and there are long exact sequences arising from pairs
Applications: Cohomology detects holes, classifies certain geometric structures (for example line and principal bundles), and provides