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