Let $M$ be a Liouville 6‐manifold which is the smooth fiber of a Lefschetz fibration on ${\mathbb{C}}^4$ constructed by suspending a Lefschetz fibration on ${\mathbb{C}}^3$. We prove that for many examples including stabilizations of Milnor fibers of hypersurface cusp singularities, the compact Fukaya category $\mathcal{F}(M)$ and the wrapped Fukaya category $\mathcal{W}(M)$ are related through $A_{\infty }$‐Koszul duality, by identifying them with cyclic and Calabi–Yau completions of the same quiver algebra. This implies the split‐generation of the compact Fukaya category $\mathcal{F}(M)$ by vanishing cycles. Moreover, new examples of Liouville manifolds which admit quasi‐dilations in the sense of Seidel–Solomon are obtained.

中文翻译：

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通过暂停Lefschetz纤维化而引起的Koszul对偶

让 $\mathrm{中号}$ 是Liouville 6流形，它是Lefschetz纤维上的光滑纤维 ${\mathbb{C}}^4$ 通过将Lefschetz纤维悬挂在 ${\mathbb{C}}^3$。我们证明，对于许多示例，包括超表面尖点奇点的Milnor纤维的稳定化，紧凑的Fukaya类$\mathcal{F}（\mathrm{中号}）$ 和包装的深谷类别 $\mathcal{w\; ^}（\mathrm{中号}）$ 通过关联 ${\mathrm{一种}}_{\infty }$‐Koszul对偶，通过将它们与同一颤动代数的循环和Calabi–Yau补全识别出来。这意味着紧凑型Fukaya类别的拆分代$\mathcal{F}（\mathrm{中号}）$通过消失的周期。此外，获得了在塞德尔-所罗门意义上允许拟扩张的Liouville流形的新例子。