  We construct an effective low energy Hamiltonian which describes fermions
dwelling on a deformed honeycomb lattice with dislocations and disclinations,
and with an arbitrary hopping parameters of the corresponding tight binding
model. It describes the interaction of fermions with a 2d gravity and has also
a local SU(2) gauge invariance of the group of rotations. We reformulate the
model as interaction of fermions with the deformation of the lattice, which
forms a phonon field. We calculate the response of fermion currents to the
external deformation or phonon field, which is a result of a Z_2 anomaly. This
can be detected experimentally.
