  Lattice formulation of a fermionic field theory defined on a randomly
triangulated compact manifold is discussed, with emphasis on the topological
problem of defining spin structures on the manifold. An explicit construction
is presented for the two-dimensional case and its relation with the Ising model
is discussed. Furthermore, an exact realization of the Kramers-Wannier duality
for the two-dimensional Ising model on the manifold is considered. The global
properties of the field are discussed. The importance of the GSO projection is
stressed. This projection has to be performed for the duality to hold.
