Characteristic classes

Characteristic classes are a fundamental concept in differential geometry and algebraic topology that provide a way to associate certain topological invariants (classes) to vector bundles. These invariants can be used to study the geometric and topological properties of manifolds and bundles. ### Key Points about Characteristic Classes: 1. **Vector Bundles**: A vector bundle is a topological construction that associates a vector space to each point of a manifold in a continuous way.