2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153606We apply the theory of finite-type invariants of homology 3-spheres to investigate the structure of the Torelli group. We construct natural cocycles in the Torelli group and show that the lower central series quotients of the Torelli group map onto a vector space of trivalent graphs. We also have analogous results for two other natural subgroups of the mapping class group.52 pages, AMSLatex, 20 figuresQuantum Algebratext