  We develop a unified framework to classify topological defects in insulators
and superconductors described by spatially modulated Bloch and Bogoliubov de
Gennes Hamiltonians. We consider Hamiltonians H(k,r) that vary slowly with
adiabatic parameters r surrounding the defect and belong to any of the ten
symmetry classes defined by time reversal symmetry and particle-hole symmetry.
The topological classes for such defects are identified, and explicit formulas
for the topological invariants are presented. We introduce a generalization of
the bulk-boundary correspondence that relates the topological classes to defect
Hamiltonians to the presence of protected gapless modes at the defect. Many
examples of line and point defects in three dimensional systems will be
discussed. These can host one dimensional chiral Dirac fermions, helical Dirac
fermions, chiral Majorana fermions and helical Majorana fermions, as well as
zero dimensional chiral and Majorana zero modes. This approach can also be used
to classify temporal pumping cycles, such as the Thouless charge pump, as well
as a fermion parity pump, which is related to the Ising non-Abelian statistics
of defects that support Majorana zero modes.
