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 to which 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.