Explicitly Computing with Fukaya Categories of Surfaces with Boundary

2025/10/13 by Grossack, Chris
#Category Theory (math.CT) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2510.10867

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.

Citations

• A geometric model for the derived category of gentle algebras
• Derived equivalences of gentle algebras via Fukaya categories
• A beginner's introduction to Fukaya categories
• Quantum groups via Hall algebras of complexes
• On differential graded categories
• Introduction to A-infinity algebras and modules
• Homological Algebra of Mirror Symmetry

Related

• On the Fukaya Categories of Higher Genus Surfaces
• A beginner's introduction to Fukaya categories
• Fukaya category on a symplectic manifold with a B-field
• Fukaya category of surfaces and mapping class group action
• Fukaya categories and deformations