THE ARNOLD CONJECTURE IN CPn AND THE CONLEY INDEX

The uploaded paper (Asselle–Izydorek–Starostka, 2022) states and proves the CP^n case of the Arnold conjecture—every Hamiltonian diffeomorphism of (CP^n, ω_FS) has at least n+1 fixed points—via a Conley index approach. This is explicit in the abstract and Theorem 1 (|Fix(φ)| ≥ n+1) and the paper positions its contribution as an alternative, purely Conley index based proof to the known results of Fortune and Floer-theoretic methods . The proof outline constructs an action functional AH on H^{1/2}(T, R^{2n+2})×R, identifies S^1-families of critical points with periodic solutions, and leverages finite-dimensional Conley index approximations, IA-homotopies, and a product formula for the relative cup-length to force at least n+1 distinct S^1-families, concluding the theorem . The candidate solution correctly recalls two standard pre-2022 proofs: (i) Fortune’s 1985 result on CP^n and (ii) the Floer-homological argument on monotone CP^n (with PSS isomorphism), yielding n+1 fixed points; the paper itself cites Fortune and situates Floer’s homological approach among prior work . Thus, the paper and the model agree on the statement; they use different proof technologies, and both are correct.