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

TL;DR

This paper establishes an equivalence between Fukaya-Seidel categories of specific Lefschetz fibrations on ^2 and the perfect derived categories of Auslander algebras of type A, enriching the understanding of their categorical and geometric structures.

Contribution

It explicitly constructs an equivalence between Fukaya-Seidel categories and derived categories of Auslander algebras of type A, connecting symplectic geometry with algebraic representation theory.

Findings

Categories are equivalent for a family of Lefschetz fibrations.

Complete description of the Milnor fibre of these fibrations.

Explicit link to partially wrapped Fukaya 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.