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In this thesis, we give a unification of the quantum WRT invariants. Given arational homology 3-sphere M and a link L inside, we define the unifiedinvariants, such that the evaluation of these invariants at a root of unityequals the corresponding quantum WRT invariant. In the SU(2) case, we assumethe order of the first homology group of the manifold to be odd. Therefore, forrational homology 3-spheres, our invariants dominate the whole set of SO(3)quantum WRT invariants and, for manifolds with the order of the first homologygroup odd, the whole set of SU(2) quantum WRT invariants. We further show, thatthe unified invariants have a strong integrality property.

Unified Quantum SO(3) and SU(2) Invariants for Rational Homology 3-Spheres