  A perturbative study of the Holstein Molecular Crystal Model which accounts
for lattice structure and dimensionality effects is presented. Antiadiabatic
conditions peculiar of narrow band materials and an intermediate to strong
electron-phonon coupling are assumed. The polaron effective mass depends
crucially in all dimensions on the intermolecular coupling strengths which also
affect the size of the lattice deformation associated with the small polaron
formation.
