Presentations of Roger and Yang's Kauffman bracket arc algebra

TL;DR

This paper presents a detailed algebraic description of Roger and Yang's Kauffman bracket arc algebra specifically for the once-punctured torus and spheres with up to three punctures.

Contribution

It offers a new presentation of the algebra for these specific surfaces, expanding understanding of their algebraic structure.

Findings

Explicit algebraic presentation for the once-punctured torus

Explicit algebraic presentation for spheres with up to three punctures

Enhanced understanding of the algebraic structure of these surfaces

Abstract

We provide a presentation of the Roger and Yang's Kauffman bracket arc algebra for the once-punctured torus and punctured spheres with three or fewer punctures.