Chern Class

A Chern class is a characteristic class defined for complex vector bundles. The Chern classes of a complex manifold are the Chern classes of its tangent bundle. For a vector bundle of bundle rank and , the th Chern class is an obstruction to the existence of everywhere complex linearly independent sections of that vector bundle. The th Chern class is in the th cohomology group of the base space (Hatcher 2017, pp. 73-78).