Topological defects in thermodynamic phases are characterized by winding
numbers of order parameters. Similarly, topological phases in the tenfold
classification of insulators and superconductors are characterized by Chern and
winding numbers. We show that both situations can be described by a single
formalism, using the notion of the symbol of the Hamiltonian which contains
all topological information. The symbol generalizes the Bloch Hamiltonian and
order parameters. Vacancies and textures in graphene are used as an example.