Characteristic classes are cohomology classes in the base space of a vector
bundle, defined through obstruction theory, which
are (perhaps partial) obstructions to the existence of 
everywhere linearly independent vector fields
on the vector bundle. The most common examples of
characteristic classes are the Chern, Pontryagin,
and Stiefel-Whitney classes.
Characteristic Class
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Cite this as:
Weisstein, Eric W. "Characteristic Class." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CharacteristicClass.html