  The lattice Dirac equation is formulated on a simplicial complex which
approximates a smooth Riemann manifold by introducing a lattice vierbein on
each site and a lattice spin connection on each link. Care is taken so the
construction applies to any smooth D-dimensional Riemannian manifold that
permits a spin connection. It is tested numerically in 2D for the projective
sphere ${\mathbb S}^2$ in the limit of an increasingly refined sequence of
triangles. The eigenspectrum and eigenvectors are shown to converge rapidly to
the exact result in the continuum limit. In addition comparison is made with
the continuum Ising conformal field theory on ${\mathbb S}^2$. Convergence is
tested for the two point, $\langle \epsilon(x_1) \epsilon(x_2) \rangle$, and
the four point, $\langle \sigma(x_1) \epsilon(x_2) \epsilon(x_3 )\sigma(x_4)
\rangle $, correlators for the energy, $\epsilon(x) = i \bar \psi(x)\psi(x)$,
and twist operators, $\sigma(x)$, respectively.
