  We calculate perturbative renormalization properties of the topological
charge, using the standard lattice discretization given by a product of twisted
plaquettes. We use the overlap and clover action for fermions, and the Symanzik
improved gluon action for 4- and 6-link loops.
  We compute the multiplicative renormalization of the topological charge
density to one loop; this involves only the gluon part of the action. The power
divergent additive renormalization of the topological susceptibility is
calculated to 3 loops.
  Our work serves also as a test case of the techniques and limitations of
lattice perturbation theory, it being the first 3-loop computation in the
literature involving overlap fermions.
