2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78253We study configurations of immersed curves in surfaces and surfaces in 3-manifolds. Among other results, we show that primitive curves have only finitely many configurations which minimize the number of double points. We give examples of minimal configurations not realized by geodesics in any hyperbolic metric.13 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon2/paper11.abs.htmlGeometric TopologyDifferential Geometry53C22, 57R42text