Definition:Cohomology Group/Motivation

Cohomology Group: Motivation

Cohomology groups arise naturally in the statement of the Poincaré Duality Theorem for Manifolds.

They are also important because the cohomology groups of a topological space $X$ can also be given ring structure.

This makes them more powerful in algebraic topology than homology.

Also see

• Results about cohomology groups can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): cohomology
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): cohomology