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

Abstract

We compute the action of the gl 2 -skein algebra of the torus on the gl 2 -skein module of the solid torus. As a result, we show that the gl 2 -skein modules of lens spaces is spanned by p 2 + 1 2 p 2 + 1 elements.