A Unified Quantum SO(3) Invariant for Rational Homology 3-Spheres

Understand

Given a rational homology 3-sphere M with the first integral homology of rank b and a link L inside M, colored by odd numbers, we construct a unified invariant I_{M,L} belonging to a modification of the Habiro ring where b is inverted.

• Our unified invariant dominates the whole set of the SO(3) Witten-Reshetikhin-Turaev invariants of the pair (M,L).
• If b=1 and L is empty, I_M coincides with Habiro's invariant of integral homology 3-spheres.
• For b>1, the unified invariant defined by the third author is determined by I_M.