 Let "g" be a smooth function on "N" vanishing at "f"("x").Then the pullback of the covector determined by "g" (denoted d"g") is given by
That is, it is the equivalence class of functions on "M" vanishing at "x" determined by "g" o "f".The "k"-th exterior power of the cotangent space, denoted Λ"k"("T""x"*"M"), is another important object in differential geometry.