为什么Landau-Ginzburg Link上同调等价于Khovanov同调？
Why Is Landau-Ginzburg Link Cohomology Equivalent To Khovanov Homology?
摘要：
在这份说明中，我们试图比较希尔伯特空间的基态在${\cal N}=(2,2)$二维朗道-金兹伯格理论的模型描述链接嵌入在${\mathbb{R}}^3$ Khovanov和Khovanov-Rozansky同源性的上同调理论。为了证实等价性，我们利用了界面的基态的Hilbert空间关于同伦的不变性。在研究Landau-Giznburg理论中的孤立子和瞬子的尝试中，我们应用了渐进分析，在文献中也称为精确WKB方法、谱网络方法或复苏。特别是，我们将LG模型中的瞬子与我们称为空网的特定WKB线配置相关联。
英文摘要：
In this note we make an attempt to compare a cohomological theory of Hilbert spaces of ground states in the ${\cal N}=(2,2)$ 2d Landau-Ginzburg theory in models describing link embeddings in ${\mathbb{R}}^3$ to Khovanov and Khovanov-Rozansky homologies. To confirm the equivalence we exploit the invariance of Hilbert spaces of ground states for interfaces with respect to homotopy. In this attempt to study solitons and instantons in the Landau-Giznburg theory we apply asymptotic analysis also known in the literature as exact WKB method, spectral networks method, or resurgence. In particular, we associate instantons in LG model to specific WKB line configurations we call null-webs.
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