Realising perfect derived categories of Auslander algebras of type A as Fukaya-Seidel categories

Abstract

We prove that the Fukaya-Seidel categories of a certain family of Lefschetz fibrations on ${\mathbb{C}}^2$ are equivalent to the perfect derived categories of Auslander algebras of Dynkin type $\mathbb{A}$. We give an explicit equivalence between these categories and the partially wrapped Fukaya categories considered by Dyckerhoff-Jasso-Lekili. We provide a complete description of the Milnor fibre of such fibrations.

51 pages, 19 figures. To appear in Journal of Symplectic Geometry (2023). Revised after referee's comments. Updated Section 3.2.2 to also give an algebraic proof of the derived equivalence of Auslander algebras of type A and ${\tilde{\Gamma }}_n$. Local changes throughout

References in corpus (1)

• Hamiltonian handleslides for Heegaard Floer homology