2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159513Pachner move 3 ->3 deals with triangulations of four-dimensional manifolds. We present an algebraic relation corresponding in a natural way to this move and based, a bit paradoxically, on three-dimensional geometry.Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/Geometric TopologyAlgebraic TopologyQuantum Algebratext