We define a fixed point action in two-dimensional lattice CPN-1 models
. The fixed point action is a classical perfect lattice action, which
is expected to show strongly reduced cutoff effects in numerical simul
ations. Furthermore, the action has scale-invariant instanton solution
s, which enables us to define a correct topological charge without top
ological defects. Using a parametrization of the fixed point action fo
r the CP3 model in a Monte Carlo simulation, we study the topological
susceptibility.