  We give a general derivation of Ginsparg-Wilson relations for both Dirac and
Majorana fermions in any dimension. These relations encode continuous and
discrete chiral, parity and time reversal anomalies and will apply to the
various classes of free fermion topological insulators and superconductors (in
the framework of a relativistic quantum field theory in Euclidean spacetime).
We show how to formulate the exact symmetries of the lattice action and the
relevant index theorems for the anomalies.
