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For every rational homology 3–sphere with H1(M, Z) = (Z/2Z)n we construct a unified invariant (which takes values in a certain cyclotomic completion of a polynomial ring), such that the evaluation of this invariant at any odd\udroot of unity provides the SO(3)Witten–Reshetikhin–Turaev invariant at this root and at any even root of unity the SU(2) quantum invariant. Moreover, this unified\udinvariant splits into a sum of the refined unified invariants dominating spin and cohomological refinements of quantum SU(2) invariants. New results on the Ohtsuki series and the integrality of quantum invariants are the main applications of our construction.\udMoreover, this unified invariant splits into a sum of the refined unified invariants dominating spin and cohomological refinements of quantum SU(2) invariants.\udNew results on the Ohtsuki series and the integrality of quantum invariants are the main applications of our construction

Unified quantum invariants and their refinements for homology 3-spheres with 2-torsion