Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Koszul duality via suspending Lefschetz fibrations   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.

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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc