  We compare the gauging of the Bargmann algebra, for the case of arbitrary
torsion, with the result that one obtains from a null-reduction of General
Relativity. Whereas the two procedures lead to the same result for
Newton-Cartan geometry with arbitrary torsion, the null-reduction of the
Einstein equations necessarily leads to Newton-Cartan gravity with zero
torsion. We show, for three space-time dimensions, how Newton-Cartan gravity
with arbitrary torsion can be obtained by starting from a Schroedinger field
theory with dynamical exponent z=2 for a complex compensating scalar and next
coupling this field theory to a z=2 Schroedinger geometry with arbitrary
torsion. The latter theory can be obtained from either a gauging of the
Schroedinger algebra, for arbitrary torsion, or from a null-reduction of
conformal gravity.
