  Specific types of spatial defects or potentials can turn monolayer graphene
into a topological material. These topological defects are classified by a
spatial dimension $D$ and they are systematically obtained from the Hamiltonian
by means of its symbol $\mathcal{H} (\boldsymbol{k}, \boldsymbol{r}) $, an
operator which generalises the Bloch Hamiltonian and contains all topological
information. This approach, when applied to Dirac operators, allows to recover
the tenfold classification of insulators and superconductors. The existence of
a stable $\mathbb{Z}$-topology is predicted as a condition on the dimension
$D$, similar to the classification of defects in thermodynamic phase
transitions. Kekule distortions, vacancies and adatoms in graphene are proposed
as examples of such defects and their topological equivalence is discussed.
