Explicitly Computing with Fukaya Categories of Surfaces with Boundary

Abstract

Fukaya categories are deep and rich invariants of symplectic manifolds which are notoriously difficult to compute explicitly. In the case of surfaces, however, the situation is simple, combinatorial,and is very well understood (at least by experts). In this expository paper we will give an introduction with many examples to welcome newcomers to the area and hopefully equip them with the tools to independently compute Fukaya categories of surfaces.

Based on a talk given at the 2025 AWM WiSCon Special Session. Major changes to figures and examples since the previous version. Comments welcome