Seifert-Torres type formulas for the Alexander polynomial from quantum sl2

We develop a diagrammatic calculus for representations of unrolled quantum sl2 at a fourth root of unity. This allows us to prove Seifert-Torres type formulas for certain splice links using quantum algebraic methods, rather than topological methods. Other applications of this diagrammatic calculus given here are a skein relation for n-cabled double crossings and a simple proof that the quantum invariant associated with these representations determines the multivariable Alexander polynomial. (c) 2022 Elsevier B.V. All rights reserved.