Fixed point action and topology in the CP$^{3}$ model

We define a fixed point action in twodimensional lattice CP^(N-1) models. The fixed point action is a classical perfect lattice action, which is expected to show strongly reduced cut-off effects in numerical simulations. Furthermore, the action has scale invariant instanton solutions, which enables us to define a correct topological charge without topological defects. Using a parametrization of the fixed point action for the CP^3 model in a Monte Carlo simulation, we study the topological susceptibility