2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115445In a previous paper, the second author defined integer-valued functions delta_n on the first cohomology of a 3-manifold, generalizing McMullen's Alexander norm. It was shown that these functions give lower bounds on the Thurston norm. In this paper, we reformulate these invariants in terms of Reidemeister torsion over a non-commutative multivariable Laurent polynomial ring. This allows us to show that these functions are semi-norms.19 pages, 4 figuresGeometric TopologyAlgebraic TopologyPrimary 57M27, Secondary 57N10text