  We consider a graphene sheet folded in an arbitrary geometry, compact or with
nanotube-like open boundaries. In the continuous limit, the Hamiltonian takes
the form of the Dirac operator, which provides a good description of the low
energy spectrum of the lattice system. We derive an index theorem that relates
the zero energy modes of the graphene sheet with the topology of the lattice.
The result coincides with analytical and numerical studies for the known cases
of fullerene molecules and carbon nanotubes and it extend to more complicated
molecules. Potential applications to topological quantum computation are
discussed.
