  This paper constructs the reduction of heterotic $M$-theory in eleven
dimensions to a supergravity model on a manifold with boundary in five
dimensions using a Calabi-Yau three-fold. New results are presented for the
boundary terms in the action and for the boundary conditions on the bulk
fields. Some general features of dualisation on a manifold with boundary are
used to explain the origin of some topological terms in the action. The effect
of gaugino condensation on the fermion boundary conditions leads to a `twist'
in the chirality of the gravitino which can provide an uplifting mechanism in
the vacuum energy to cancel the cosmological constant after moduli
stabilisation.
