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 cut-off effects in numerical simu
lations. Furthermore, the action has scale invariant instanton solutio
ns, which enables us to define a topological charge without topologica
l defects. We present results for the scaling of the topological sucep
tibility from a Monte Carlo simulation in the CP3 model.