$\mathfrak{gl}(1 \vert 1)$-Alexander polynomial for $3$-manifolds, Reidemeister torsion and lens spaces

Abstract

In this note, we reformulate the invariant $\Delta (M, \omega)$ that we defined before, and show its relation with Reidemeister torsion. We calculate $\Delta (M, \omega)$ when the $3$-manifolds are lens spaces, and discuss the classification of the lens spaces using $\Delta (M, \omega)$.