We construct an invariant JM of integral homology spheres M with values in a completion Ẑ[q] of the polynomial ring Z[q] such that the evaluation at each root of unity ζ gives the the SU(2) Witten-ReshetikhinTuraev invariant τζ(M) of M at ζ. Thus JM unifies all the SU(2) WittenReshetikhin-Turaev invariants of M . As a consequence, τζ(M) is an algebraic integer. Moreover, it follows that τζ(M) a...