Characteristic classes

Characteristic class

In mathematics, a characteristic class is a way of associating to each principal bundle of X a cohomology class of X. The cohomology class measures the extent the bundle is "twisted" and whether it possesses sections. Characteristic classes are global invariants that measure the deviation of a local product structure from a global product structure. They are one of the unifying geometric concepts in algebraic topology, differential geometry, and algebraic geometry. The notion of characteristic class arose in 1935 in the work of Eduard Stiefel and Hassler Whitney about vector fields on manifolds. (Wikipedia).

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Pontryagin class | Shiing-Shen Chern | Principal bundle | Differential form | Homotopy | Unitary group | Maximal torus | Hassler Whitney | Monomial | K-theory | Continuous function | Topological group | Italian school of algebraic geometry | Algebraic topology | CW complex | Isomorphism class | Section (category theory) | Cohomology | Segre class | Gauss–Bonnet theorem | Grassmannian | Classifying space | Obstruction theory | Pullback bundle | Euler characteristic | Homotopy theory | Stiefel–Whitney class | Euler class | Principle of locality | Natural transformation | De Rham cohomology | Cup product | Homology (mathematics) | Mathematics | Set (mathematics) | Function (mathematics) | Algebraic geometry | Fundamental class | Instanton | Section (fiber bundle) | Vector bundle | Cobordism | Category (mathematics) | Manifold | Orthogonal group | Curvature | Chern class | Differential geometry | Stable homotopy theory | Schubert calculus | Foliation | Covariance