2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78807Delta finite-type invariants are defined analogously to finite-type invariants, using delta moves instead of crossing changes. We show that they are closely related to the lower central series of the commutator subgroup of the pure braid group.6 pages, 2 figures, based on talk given in Delphi, August 1998Geometric TopologyQuantum Algebra57M25Braid commutators and delta finite-type invariantstext