2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63361We study torus actions on symplectic manifolds with proper moment maps in the case that each reduced space is two-dimensional. We provide a complete set of invariants for such spaces. Our proof uses sheaves of groupoids of Hamiltonian spaces.Final version, to appear in the Journal of Symplectic Geometry. Previous title: Tall complexity one Hamiltonian torus actions. Revisions: improved expositionSymplectic GeometryDifferential GeometryGeometric Topology53D20;53D35text