2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67774This survey covers earlier work of the author as well as recent work on Riemann's moduli space, its canonical cell decomposition and compactification, and the related operadic structure of arc complexes.36 pages, 13 figuresGeometric TopologyDifferential Geometry32G15,30F60,14H15Cell decomposition and compactification of Riemann's moduli space in decorated Teichmüller theorytext