ABSTRACT
We introduce a notion of finite type invariants of oriented rational homology 3-spheres. We show that the map to finite type invariants of integral homology 3-spheres is one-to-one and deduce that the space of finite type invariants of rational homology 3-spheres is a filtered commutative algebra with finite dimensional non-zero graded quotients only in degrees divisible by 3. We show that the Casson-Walker invariant is of type 3. We mention an alternative B-finite-type notion of invariants of rational homology 3-spheres, with “better grading” properties, and show that type 3m invariants of rational homology 3-spheres are included in B-type m invariants. Finally, we prove a non-existence theorem for finite type invariants of oriented, closed 3-manifolds.
