2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228076A homeomorphism of a 3-manifold M is said to be Dehn twists on the boundary when its restriction to the boundary of M is isotopic to the identity on the complement of a collection of disjoint simple closed curves in the boundary of M. In this paper, we give various results about such collections of curves and the associated homeomorphisms. In particular, if M is compact, orientable, irreducible and the boundary of M is a single torus, and M admits a homeomorphism which is a nontrivial Dehn twist on the boundary of M, then M must be a solid torus.This is the version published by Algebraic & Geometric Topology on 20 September 2006Geometric Topology57M99, 57R50text