Hamiltonian No-Torsion

The paper proves that on closed negative monotone or symplectically Calabi–Yau manifolds, every finite-group homomorphism into Ham(M,ω) is trivial (Theorem B), by combining: (i) that any prime-order Hamiltonian torsion element is weakly non-degenerate generalized perfect (Theorem C) and (ii) that such diffeomorphisms cannot exist on negative monotone or symplectically Calabi–Yau manifolds (Theorem D). An explicit remark notes that, via Cauchy’s theorem, ruling out prime-order torsion suffices to forbid all finite subgroups, yielding Theorem B . The candidate solution uses precisely this chain (Cauchy → Theorem C → Theorem D → triviality), so its logic aligns with the paper. One overstatement in the candidate is that the “global Floer differential vanishes” for p-torsion; Theorem C establishes a Floer–Morse–Bott and generalized perfect structure, but does not by itself assert vanishing of the global differential. This point is not used in the candidate’s actual deduction, so the main conclusion remains correct. The auxiliary observation that Cauchy’s theorem furnishes a prime-order element in any nontrivial finite subgroup matches the paper’s own remark .