  The present work has two goals. The first is to complete the classification
of geometries in terms of torsion classes of M-branes wrapping cycles of a
Calabi-Yau. The second goal is to give insight into the physical meaning of the
torsion class constraints. We accomplish both tasks by defining new energy
minimizing calibrations in M-brane backgrounds. When fluxes are turned on, it
is these calibrations that are relevant, rather than those which had previously
been defined in the context of purely geometric backgrounds.
