A gadget defined for complex vector bundles. The Chern classes of a complex manifold are the Chern classes of its tangent bundle. The th Chern class is an obstruction to the existence of everywhere complex linearly independent vector fields on that vector bundle. The th Chern class is in the th cohomology group of the base space.
Chern Class
See also
Chern Number, Obstruction, Pontryagin Class, Stiefel-Whitney ClassExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Chern Class." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ChernClass.html