# The Hall Algebras of Annuli

## TL;DR

This paper computes the derived Hall algebras of Fukaya categories of annuli with multiple marked intervals, confirming a key conjecture and advancing understanding of their algebraic structures.

## Contribution

It refines and proves the main conjecture for annuli with multiple marked intervals by explicitly computing their derived Hall algebras.

## Key findings

- Derived Hall algebras of annuli are explicitly computed.
- The central conjecture is confirmed for annuli with at least two marked intervals.
- Advances understanding of Fukaya categories and their algebraic properties.

## Abstract

We refine and prove the central conjecture of our first paper for annuli with at least two marked intervals on each boundary component by computing the derived Hall algebras of their Fukaya categories.