The Rohlin invariant and ℤ/2-valued invariants of homology spheres

Abstract

In this paper we prove that the Rohlin invariant is the unique invariant inducing a homomorphism on the Torelli group. Using this result we generalize the construction of invariants of homology [Formula: see text]-spheres from families of trivial 2-cocycles on the Torelli group given by Pitsch to include invariants with values on an abelian group with [Formula: see text]-torsion.