2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58637We describe a contact analog of the symplectic cut construction. As an application we show that the group of contactomorphisms for a particular overtwisted contact structure on the three sphere contains countably many nonconjugate two tori.(v2) Following referee's suggestions the paper is expanded. The local cut construction is made more precise. A theorem concerning the group of contactomorphisms of certain overtwisted lens spaces is addedSymplectic GeometryDifferential Geometrytext