Open Research Index

Hamiltonian Fixed Points Below the Stable Morse Number

OpenAI

OpenAI Mathopenai-math/Hamiltonian-Fixed-Points-Below-the-Stable-Morse-NumberOct 5, 2026math.DGAI-generatedscore 0

We disprove the stable Morse lower bound for nondegenerate Hamiltonian fixed points by constructing a simply connected closed Kähler manifold with sixteen fewer fixed points than its stable Morse number. All the corresponding periodic orbits are contractible. The construction combines a Hamiltonian involution with integral homology torsion at two different primes; its proof uses finite-dimensional Morse theory and complex blowups.

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