2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112941We study the relationship between trivial cocycles on the Torelli group and invariants of oriented integral homology 3-spheres. We give ncecessary and sufficient conditions for a function defined on the union of the Torelli groups to be an invariant of homology spheres. We apply this study to give a new purely algebraic construction of the Casson invariant and prove in this setting its surgery properties. As a by-product we get a new 2-torsion cohomology class in the second integral cohomology of the Torelli group.25 pages, 12 figuresGeometric TopologyK-Theory and Homology57M27 (Primary); 20J05 (Secondary)text