We define Lagrangian Floer cohomology over ${\mathbb{Z}}_2$-coefficients by counting pearly trajectories for graded, exact Lagrangian immersions that satisfy a certain positivity condition on the index of the non-embedded points, and show that it is an invariant of the Lagrangian immersion under Hamiltonian deformations. We also show that it is naturally isomorphic to the Hamiltonian perturbed version of Lagrangian Floer cohomology as defined in [4]. As an application, we prove that the number of non-embedded points of such a Lagrangian in ${\mathbb{C}}^n$ is no less than the sum of its Betti numbers.

中文翻译：

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通过珍珠轨迹浸入拉格朗日 Floer 上同调

我们定义拉格朗日 Floer 上同调 ${\mathbb{Z}}_2$-通过计算满足非嵌入点索引的特定正条件的分级精确拉格朗日浸入的珍珠轨迹的系数，并表明它是哈密顿变形下拉格朗日浸入的不变量。我们还表明，它与 [4] 中定义的拉格朗日 Floer 上同调的哈密顿量扰动版本自然同构。作为一个应用，我们证明了这样一个拉格朗日函数的非嵌入点数${\mathbb{C}}^n$ 不小于其 Betti 数之和。