  Based on the geometric interpretation of the Dirac equation as an evolution
equation on the three-dimensional exterior bundle /(R^3), we propose the bundle
(T x / x /)(R^3) as a geometric interpretation of all standard model fermions.
The generalization to curved background requires an ADM decomposition M^4=M^3 x
R and gives the bundle (T x / x /)(M^3). As a consequence of the geometric
character of the bundle there is no necessity to introduce a tetrad or triad
formalism. Our space-geometric interpretation associates colors as well as
fermion generations with directions in space, electromagnetic charge with the
degree of a differential form, and weak interactions with the Hodge star
operator.
  The space-geometric interpretation leads to different physical predictions
about the connection of the SM with gravity, but gives no such differences on
Minkowski background.
