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

Abstract

As an extension of Reshetikhin and Turaev’s invariant, Costantino, Geer and Patureau-Mirand constructed 3-manifold invariants in the setting of relative [Formula: see text]-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 3-manifold invariant from Viro’s [Formula: see text]-Alexander polynomial. We take lens spaces [Formula: see text] and [Formula: see text] as examples to show that this invariant can distinguish homotopy equivalent manifolds.