The ${\mathfrak{gl}}_2$-Skein Module of Lens Spaces via the Torus and Solid Torus

Abstract

We compute the action of the ${\mathfrak{gl}}_2$-skein algebra of the torus on the ${\mathfrak{gl}}_2$-skein module of the solid torus. As a result, we show that the ${\mathfrak{gl}}_2$-skein modules of lens spaces is spanned by $\left(\lfloor \frac{p}{2}\rfloor +1\right)\left(2\lfloor \frac{p}{2}\rfloor +1\right)$ elements.

26 pages