2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70033The modular envelope of a cyclic operad is the smallest modular operad containing it. A modular operad is constructed from moduli spaces of Riemann surfaces with boundary; this modular operad is shown to be the modular envelope of the A-infinity cyclic operad. This gives a new proof of the result of Harer-Mumford-Thurston-Penner-Kontsevich that a cell complex built from ribbon graphs is homotopy equivalent to the moduli space of curves.14 pages. Version 2: references added, proofs cleaned upAlgebraic GeometryQuantum Algebratext