  In the Bargmann-Fock representation the coordinates $z^i$ act as bosonic
creation operators while the partial derivatives $\partial_{z^j}$ act as
annihilation operators on holomorphic $0$-forms as states of a $D$-dimensional
bosonic oscillator. Considering also $p$-forms and further geometrical objects
as the exterior derivative and Lie derivatives on a holomorphic ${\bf C}^D$, we
end up with an analogous representation for the $D$-dimensional supersymmetric
oscillator. In particular, the supersymmetry multiplet structure of the Hilbert
space corresponds to the cohomology of the exterior derivative. In addition, a
1-complex parameter group emerges naturally and contains both time evolution
and a homotopy related to cohomology. Emphasis is on calculus.
