  We show that a class of fermion theory formulated on a compact, curved
manifold will generate a condensate whose magnitude is determined only by the
volume and Euler characteristic of the space. The construction requires that
the fermions be treated as K\"{a}hler-Dirac fields and the condensate arises
from an anomaly associated with a $U(1)$ global symmetry which is subsequently
broken to a discrete subgroup. Remarkably the anomaly survives under
discretization of the space which allows us to compute the condensate on an
arbitrary triangulation. The results, being topological in character, should
hold in a wide range of gravitationally coupled fermion theories both classical
and quantum
