The difference of two connections on a vector bundle is a global endomorphism-valued one-form. Taking the trace of the curvature difference formula cancels both the commutator terms and the trace of the square of that one-form. Consequently the trace curvatures represent the same de Rham cohomology class.

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  1. Curvature difference formula
  2. Curvature form of a connection
  3. Connection on a vector bundle
  4. Vector bundle
  5. Fiber bundle
  6. Algebraic topology
  7. Geometry and topology
  8. Area of mathematics
  9. Mathematics
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