2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67452We present a sketch of the proof of the following theorems: (1) Every 3-manifold has only finitely many homotopy classes of 2-plane fields which carry tight contact structures. (2) Every closed atoroidal 3-manifold carries finitely many isotopy classes of tight contact structures.12 pages, to appear in the 2001 Georgia International Topology Conference proceedingsGeometric TopologyDifferential GeometrySymplectic Geometry53D35text