复梯度流方程与Seidel谱序列
The Complex Gradient Flow Equation and Seidel's Spectral Sequence
摘要：
根据Donaldson-Thomas，Haydys和Gaiotto-Moore-Witten的建议，我们利用复梯度流方程对一类合适的Morse Landau-Ginzburg模型构造了一个M-S范畴，该范畴具有推广到无穷维的潜力.在构造的过程中，我们给出了Seidel关于Lagrangian Floer上同调的谱序列的另一种证明，它可以被看作是一个潜在的有边的E-Floer理论的有限维模型.关键的观察是，在颈拉伸极限下，这个复杂的梯度流方程在Floer上链复形上产生自然的几何过滤。由此产生的谱序列，然后确定与赛德尔的原始之一。
英文摘要：
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.
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