Cartan's method of the Repere Mobile can be used to construct most of the
theorems of Fiber bundle theory and connections. The Cartan equations of
structure can be determined in a constructive manner. In particular, the
technique leads to an algebraic method of computing matrix of curvature 2-forms
and the vectors of torsion 2-forms.
More over the method demonstrates that there are two types of torsion 2-forms -
a torsion 2-form of translations (affine) and a torsion 2-form of rotations.
The latter equation of structure is often ignored, but can be used to develop a
theory of disclinations.