Nine generators of the skein space of the $3$–torus

Abstract

We show that the skein vector space of the $3$–torus is finitely generated. We show that it is generated by nine elements: the empty set, some simple closed curves representing the nonzero elements of the first homology group with coefficients in ${\mathbb{Z}}_2$, and a link consisting of two parallel copies of one of the previous nonempty knots.