论文标题
复杂的梯度流程方程和Seidel的光谱序列
The Complex Gradient Flow Equation and Seidel's Spectral Sequence
论文作者
论文摘要
根据Donaldson-Thomas，Haydys和Gaiotto-Moore-Witten的提议，我们使用复杂的梯度流程方程为合适的Morse Landau-Ginzburg模型提供了Fukaya-Seidel类别的构造，这具有对某些无限尺寸示例的潜力。 在这种结构的过程中，我们为拉格朗日浮点数的Seidel光谱序列提供了替代证明，可以将其视为潜在边界的单极浮子理论的有限维度模型。关键的观察结果是，在颈部拉伸极限下，这种复杂的梯度流程方程在浮球割线复合物上产生了自然的几何过滤。然后用Seidel的原始光谱序列识别。
Following the proposals of Donaldson-Thomas, Haydys and Gaiotto-Moore-Witten, we give a construction of Fukaya-Seidel categories for a suitable class of Morse Landau-Ginzburg models using the complex gradient flow equation, which has the potential for generalization to some infinite dimensional examples. In the course of this construction, we give an alternative proof to Seidel's spectral sequence for Lagrangian Floer cohomology, which can be viewed as a finite dimensional model for a potential bordered monopole Floer theory. The key observation is that under a neck-stretching limit, this complex gradient flow equation produces a natural geometric filtration on the Floer cochain complex. The resulting spectral sequence is then identified with Seidel's original one.
