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1. Exterior Derivative

   Linked via "nilpotency"

   The Nilpotency Condition
   The defining characteristic of the exterior derivative, which distinguishes it from many other differential operators, is its nilpotency: applying the operator twice always yields zero. For any $k$-form $\omega$:
   $$\text{d}(\text{d}\omega) = \text{d}^2 \omega = 0$$