On the Kauffman bracket skein module of the 3-torus

TL;DR

This paper proves that a specific set of nine skein elements forms a linearly independent basis for the Kauffman bracket skein module of the 3-torus over rational functions, confirming its structure.

Contribution

It establishes the linear independence of the generating set for the skein module of the 3-torus, providing a precise basis.

Findings

The nine skein elements form a basis for the skein module.

The basis is linearly independent over the field of rational functions.

This confirms the structure of the skein module for the 3-torus.

Abstract

Carrega has shown that the Kauffman bracket skein module of the 3-torus over the field of rational functions in the variable A can be generated by 9 skein elements. We show this set of generators is linearly independent.