Explore: Chern Classes

topology, differential geometry and algebraic geometry, the Chern classes are characteristic classes associated with complex vector bundles. They have since

Chern's work, most notably the Chern–Gauss–Bonnet theorem, Chern–Simons theory, and Chern classes, are still highly influential in current research in mathematics

In mathematics, the Chern–Weil homomorphism is a basic construction in Chern–Weil theory that computes topological invariants of vector bundles and principal

bundle can be defined by means of the theory of Chern classes, and is encountered where Chern classes exist — most notably in differential topology, the

In mathematics, the Chern–Simons forms are certain secondary characteristic classes. The theory is named for Shiing-Shen Chern and James Harris Simons

2004, p. 141, Proposition 2.2.6.) For a variety X over a field, the Chern classes of any vector bundle on X act by cap product on the Chow groups of X

+c_{i-1}(A)c_{1}(C)+c_{i}(C).} It follows that the Chern classes of a vector bundle E {\displaystyle E} depend only on the class of E {\displaystyle E} in the Grothendieck

Pontryagin classes. The Pontryagin classes of a complex vector bundle π : E → X {\displaystyle \pi :E\to X} is completely determined by its Chern classes. This

{\mathcal {E}}''\to 0} . The Euler sequence can be used to compute the Chern classes of projective space. Recall that given a short exact sequence of coherent

fundamental characteristic classes known at that time (the Stiefel–Whitney class, the Chern class, and the Pontryagin classes) were reflections of the classical