Georgia Institute of Technology College of Sciences

Unlike the integral case, given a prime number p, not all Z/p-homology 3-spheres can be constructed as a Heegaard splitting with a gluing map an element of mod p Torelli group, M[p]. Nevertheless, letting p vary we can get any rational homology 3-sphere. This motivated us to study invariants of rational homology 3-spheres that comes from M[p]. In this talk we present an algebraic tool to construct invariants of rational homology 3-spheres from a family of 2-cocycles on M[p]. Then we apply this tool to give all possible invariants that are induced by a lift to M[p] of a family of 2-cocycles on the abelianization of M[p], getting a family of invariants that we will describe precisely.