2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61944We introduce the notion of a `canonical' splitting over Z or ZxZ for a finitely generated group G. We show that when G happens to be the fundamental group of an orientable Haken manifold M with incompressible boundary, then the decomposition of the group naturally obtained from canonical splittings is closely related to the one given by the standard JSJ-decomposition of M. This leads to a new proof of Johannson's Deformation Theorem.We have another paper in preparation which contains far more general algebraic resultsGeometric TopologyGroup Theory57M07;57N10;20E06text