2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77382For a smooth oriented surface S, denote by M(S) the set of all ways to represent S as a result of gluing together standard spheres with holes (``the Lego game''). In this paper we give a full set of simple moves and relations which turn M(S) into a connected and simply-connected 2-complex. Results of this kind were first obtained by Moore and Seiberg, but their paper contains serious gaps. Our proof is based on a different approach and is much more rigorous.33 pages, lots of figures, LaTeX2eGeometric TopologyQuantum Algebratext