Closure conjecture for graded gentle algebras under derived equivalence

Let S=(S,Σ,η)\mathbf S=(S,\Sigma,\eta) be a graded smooth surface with stops, and let W(S)\mathcal W(\mathbf S) denote its partially wrapped Fukaya category. A formal generator is a generator of W(S)\mathcal W(\mathbf S) whose associated endomorphism AA_\infty algebra is formal. Gentle-algebra closure conjecture. The class of graded gentle algebras is closed under derived equivalence. In particular, every formal generator of W(S)\mathcal W(\mathbf S) is given by a formal dissection of S\mathbf S. This is presented as the folklore smooth-surface case of the broader conjecture for graded orbifold surfaces; the paper notes that the analogous orbifold statement is known for disks with one orbifold point and stops, but the general closure claim remains open.

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Primary source

Severin Barmeier, Sibylle Schroll and Zhengfang Wang, “Partially wrapped Fukaya categories of orbifold surfaces”, arXiv:2407.16358 (2024).

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