Symplectic higher Auslander correspondence for type A

Abstract

We prove that the Fukaya-Seidel categories of a certain family of singularities on ${\mathbb{C}}^d$ are equivalent to the perfect derived categories of higher Auslander algebras of Dynkin type A. We relate these to the Fukaya-Seidel categories of Brieskorn-Pham singularities and to the partially wrapped Fukaya categories considered by Dyckerhoff-Jasso-Lekili. We provide a symplectic interpretation to higher Auslander correspondence of type A in terms of Fukaya-Seidel categories of Lefschetz fibrations.

67 pages, 22 figures. (v3) Incorporated referee comments and thesis corrections. Fixed gap in proof of Proposition 3.16 (now 3.45). Added new section comparing $f_{n,d}$ and ${\Phi }_{n,d}$. Expanded arguments, improved exposition, minor changes throughout. Accepted version, to appear in Quantum Topology