9 generators of the skein space of the 3-torus

TL;DR

This paper proves that the skein vector space of the 3-torus is finitely generated by nine specific elements, including the empty set, certain simple closed curves, and a particular link, advancing understanding of its algebraic structure.

Contribution

It establishes that the skein space of the 3-torus is finitely generated and explicitly identifies the nine generators, a novel result in the study of skein modules.

Findings

The skein space of the 3-torus is finitely generated.

Nine specific generators are sufficient for the skein space.

The generators include the empty set, certain curves, and a specific link.

Abstract

We show that the skein vector space of the 3-torus is finitely generated. We show that it is generated by 9 elements: the empty set, some simple closed curves representing the non null elements of the first homology group with coefficients in \Z_2, and a link consisting of two parallel copies of one of the previous non empty knots.