Unified quantum invariants for integral homology spheres associated with simple Lie algebras (Q321676)

In the paper under review the authors construct an invariant of integral homology spheres, with values in the cyclotomic completion of \(\mathbb{Z}[q]\), such that the evaluation of this invariant at a fixed root of unity gives the corresponding Witten-Reshetikhin-Turaev (WRT) invariant. In this way the new invariant unifies WRT quantum invariants and also represents them as a kind of an ``analytic function'' defined on the set of roots of unity. Consequently, this implies that WRT quantum invariants are algebraic integers and are determined by the Ohtsuki series and hence by Lê-Murakami-Ohtsuki invariants.