Cohomology Theory
The Chern-Gauss-Bonnet Theorem connects the topology of a manifold to its geometry, stating that the integral of the Euler characteristic over a compact, oriented Riemannian manifold is equal to the integral of a specific polynomial expression of its curvature. This theorem reveals deep relationships between curvature, topology, and Chern classes, illustrating how geometric properties can influence topological invariants.
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