{"id":"openai-math/Sharpness-of-the-Cyclic-Integral-Floer-Bound-Below-the-Stable-Morse-Number","pdf":"https://github.com/openai/math/blob/main/preprints/Sharpness-of-the-Cyclic-Integral-Floer-Bound-Below-the-Stable-Morse-Number-October-5-2026/sharp-cyclic-integral-floer-bound-below-stable-morse-number.pdf","url":"https://github.com/openai/math/tree/main/preprints/Sharpness-of-the-Cyclic-Integral-Floer-Bound-Below-the-Stable-Morse-Number-October-5-2026","tags":["symplectic-geometry","floer-homology","hamiltonian-dynamics","morse-theory"],"score":0,"title":"Sharpness of the Cyclic Integral Floer Bound Below the Stable Morse Number","domain":"Differential geometry","family":"347","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"We construct a simply connected closed Kähler manifold of real dimension 3332 and minimal Chern number one whose Hamiltonian fixed-point count attains the cyclic integral Floer bound while falling below the stable Morse number. The Hamiltonian diffeomorphism has exactly $`1\\,872\\,232`$ fixed points, all nondegenerate and with contractible orbit loops, whereas the stable Morse number is $`1\\,872\\,264`$. Thus the stronger stable Morse bound fails by exactly 32, even when the cyclic integral bound is sharp.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Counterexamples to stable-Morse and strong Arnold fixed-point bounds"}