Editing Characteristic class (section)

{{Use American English|date=January 2019}}{{Short description|Association of cohomology classes to principal bundles
}}
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 [[section (fiber bundle)|section]]s. Characteristic classes are global [[topological invariant|invariant]]s that measure the deviation of a [[principle of locality|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.