Hamiltonian Fixed Points Below the Stable Morse Number in Dimension Twenty-Two
We disprove the stable Morse lower bound for nondegenerate Hamiltonian fixed points with examples in fixed real dimension twenty-two. For every integer m ≥ 1, we construct a simply connected closed Kähler manifold with stable Morse number $80+1968m$ and a Hamiltonian diffeomorphism with exactly $80+1952m$ fixed points, all nondegenerate and with contractible orbit loops. The deficit is therefore unbounded, and the fixed-point count is at most 127/128 of the stable Morse number.
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