# Farey recursion and the character varieties for 2-bridge knots

## TL;DR

This paper characterizes the SL(2,C) and diagonal character varieties of all 2-bridge knots and links using polynomials derived from Farey recursion, providing a unified algebraic framework.

## Contribution

It introduces a novel approach to describe character varieties of 2-bridge knots and links via Farey recursion-based polynomials, unifying their algebraic structure.

## Key findings

- Explicit polynomial descriptions for all 2-bridge knot character varieties
- Unified algebraic framework for knots and links
- Application of Farey recursion to algebraic geometry of knot complements

## Abstract

We describe the (P)SL(2,C) character varieties of all 2-bridge knots and the diagonal character varieties for all 2-bridge links in terms of a set of polynomials defined using Farey recursion.