The recent work Su and Wagner  defines cuts and flows of a regular matroid (i.e., one represented by a totally unimodular matrix M); when M is the boundary matrix of a cell complex, this is the case where the torsion coefficients are all trivial.
(Note that if indeed d = 1, then all the torsion coefficients are 1; [mu] is just the number of vertices of [SIGMA]; and for any edge [sigma] in [gamma], the vector [chi]([gamma], [sigma]) is the usual signed characteristic vector of the fundamental bond bo([gamma], [sigma]).)
The [i.sup.th] reduced Betti number is [[??].sub.i]([SIGMA]) = dim [H.sub.i]([SIGMA]; Q), and the [i.sup.th] torsion coefficient [t.sub.i]([SIGMA]) is the cardinality of the torsion subgroup T([[??].sub.i]([SIGMA]; Z)).