2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149541This paper compares the definitions of finite-type invariants due to Ohtsuki and to Garoufalidis, showing that, residually, type 3m of the former equals type m of the latter. It also shows that type 2m Ohtsuki invariants define knot invariants of type 3m (first proved by Habegger).13 pages, PostscriptQuantum AlgebraOn Finite Type 3-manifold invariants IV: Comparison of Definitionstext