稳定Morse数之下循环积分Floer界的尖锐性
Sharpness of the Cyclic Integral Floer Bound Below the Stable Morse Number
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具体内容
稿件研究Hamiltonian不动点计数中循环积分Floer界与稳定Morse界的关系。作者声称构造实维数3332、最小Chern数为1的单连通闭Kähler流形，其上Hamiltonian微分同胚恰有1,872,232个不动点，全部非退化且轨道环路可缩，而稳定Morse数为1,872,264。摘要表示循环积分界达到尖锐时，更强的稳定Morse界仍恰好差32而失效。
- 构造实维数3332、最小Chern数为1的单连通闭Kähler流形
- Hamiltonian微分同胚恰有1,872,232个非退化不动点，轨道环路可缩
- 稳定Morse数为1,872,264，更强界恰好差32而失效
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英文原始摘要
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.
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