  We 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.
