2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167363To a closed braid in a solid torus we associate a trace graph in a thickened torus in such a way that closed braids are isotopic if and only if their trace graphs can be related by trihedral and tetraherdal moves. For closed braids with a fixed number of strands, we recognize trace graphs up to isotopy and trihedral moves in polynomial time with respect to the braid length.20 pages, 15 figuresGeometric TopologyAlgebraic Topology57M25text