http://mathworld.wolfram.com/ChernClass.html
This is a secondary source, which give me the definition of what Chern Class is.
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.
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