Gl(1|1)-Alexander polynomial for 3-manifolds

As an extension of Reshetikhin and Turaev's invariant, Costantino, Geer and Patureau-Mirand constructed gl3-manifold invariants in the setting of relative glG-modular categories, which include both semi-simple and non-semi-simple ribbon tensor categories as examples. In this paper, we follow their method to construct a gl3-manifold invariant from Viro's gl(1|1)-Alexander polynomial. We take lens spaces glL(7, 1) and glL(7, 2) as examples to show that this invariant can distinguish homotopy equivalent manifolds.