Chern-Weil theory

In mathematics, Chern-Weil theory computes topology invariants of vector bundles and principal bundles in terms of connections and curvature. That is, the theory forms a bridge between the areas of algebraic topology and differential geometry. It was developed in the late 1940s by Shiing-Shen Chern and André Weil, in the wake of proofs of the generalized Gauss-Bonnet theorem.

See Chern-Weil homomorphism for more detail.