Cohomology of Lie groups

Summary

The cohomology of a Lie group $G$ is the singular cohomology of its underlying manifold, with the extra structure given by the group multiplication. The multiplication makes it a Hopf algebra, which strongly restricts its form. For a compact connected group, real cohomology can be computed from invariant differential forms, that is, from the cohomology of the Lie algebra. This turns a topological question into a question of linear algebra.