 and second,
 and second,   churn class.
  churn class.
Characteristic classes are a property of the bundle rather than the particular connection on the bundle.
Defined in terms of invariant polynomials.
characteristic class: collection of classes that depends on bundle
but not on a choice of connection.   
 
  is a homomorphism, known as the Weil homomorphism.
  is a homomorphism, known as the Weil homomorphism.