1. A mathematical theory in algebraic topology that assigns algebraic structures (such as groups or rings) to topological spaces, used to study their properties and classify them.
Usage: technical; mathematics; advanced undergraduate and graduate level

Examples

• Cohomology provides a powerful tool for distinguishing between different topological spaces.
• The de Rham cohomology of a manifold encodes information about its differential structure.
• Singular cohomology is one of the most commonly studied variants in algebraic topology.
• Researchers used cohomology theory to prove that the two spaces were not homeomorphic.
• Sheaf cohomology extends classical cohomology to more general settings in algebraic geometry.