论文标题
阿诺德猜想整数
Arnold conjecture over integers
论文作者
论文摘要
对于任何封闭的符号歧管，我们表明，非排定汉密尔顿的1个周期轨道的数量是从下面界定的，这是在Q和所有特征性的tortions的总betti数字上的总betti数字。该证明是基于用整数系数在Novikov环上构建Hamiltonian浮子理论的基础，该理论概括了我们早期构建整数值Gromov-witten类型不变性的工作。在构造过程中，我们建立了一个具有兼容的平滑全球库兰尼图表的哈密顿浮动流量类别。这概括了最近的Abouzaid-McLean-Smith的工作，这可能具有独立的兴趣。
For any closed symplectic manifold, we show that the number of 1-periodic orbits of a nondegenerate Hamiltonian thereon is bounded from below by a version of total Betti number over Z of the ambient space taking account of the total Betti number over Q and torsions of all characteristic. The proof is based on constructing a Hamiltonian Floer theory over the Novikov ring with integer coefficients, which generalizes our earlier work for constructing integer-valued Gromov-Witten type invariants. In the course of the construction, we build a Hamiltonian Floer flow category with compatible smooth global Kuranishi charts. This generalizes a recent work of Abouzaid-McLean-Smith, which might be of independent interest.
