Chern Class

A Gadget defined for Complex Vector Bundles. The Chern classes of a Complex Manifold are the Chern classes of its Tangent Bundle. The $i$th Chern class is an Obstruction to the existence of $(n-i+1)$ everywhere Complex linearly independent Vector Fields on that Vector Bundle. The $i$th Chern class is in the $(2i)$th cohomology group of the base Space.

See also Obstruction, Pontryagin Class, Stiefel-Whitney Class