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We define a fixed point action in two-dimensional lattice ${\rm CP}^{N-1}$models. The fixed point action is a classical perfect lattice action, which isexpected to show strongly reduced cutoff effects in numerical simulations.Furthermore, the action has scale-invariant instanton solutions, which enablesus to define a correct topological charge without topological defects. Using aparametrization of the fixed point action for the ${\rm CP}^{3}$ model in aMonte Carlo simulation, we study the topological susceptibility.Comment: 27 pages, 5 figures, typeset using REVTEX, Sec. 6 rewritten  (additional numerical results), to be published in Phys.Rev.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

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Fixed point action and topology in the CP3model