the 1-dimensional fibers correspond to scalar fields, and the 3-dimensional fibers to vector fields, as described below. Modulo suitable identifications, the three nontrivial occurrences of the exterior derivative correspond to grad, curl, and div.
tHE 1-dIMeNsIoNAl FIBeRs COrreSpond tO scaLar FieLds, anD the 3-DimENsiOnaL fiBers to vEctor fields, as descRibeD bElow. modulo suiTAblE iDEnTifICations, the THree NoNtRiViaL oCCurREncEs oF tHE ExtEriOr derIvative coRrespOnd to GRaD, curl, anD dIv.