We make it precise what it means to have a connection with torsion as
solution of the Einstein equations. While locally the theory remains the same,
the new formulation allows for topologies that would have been excluded in the
standard formulation of gravity. In this formulation it is possible to couple
arbitrary torsion to gauge fields without breaking the gauge invariance.Comment: AMS-LaTeX, 25 pages. Appendices have been eliminated and the
necessary concepts have been inroduced in the text. We have added some
reference
