  We interpret heterotic M-theory in terms of h-cobordism, that is the
eleven-manifold is a product of the ten-manifold times an interval is
translated into a statement that the former is a cobordism of the latter which
is a homtopy equivalence. In the non-simply connected case, which is important
for model building, the interpretation is then in terms of s-cobordism, so that
the cobordism is a simple-homotopy equivalence. This gives constraints on the
possible cobordisms depending on the fundamental groups and hence provides a
characterization of possible compactification manifolds using the Whitehead
group-- a quotient of algebraic K-theory of the integral group ring of the
fundamental group-- and a distinguished element, the Whitehead torsion. We also
consider the effect on the dynamics via diffeomorphisms and general dimensional
reduction, and comment on the effect on F-theory compactifications.
