Unified Witten-Reshetikhin-Turaev Invariants for Homology Spheres
by Andrei Ratiu
Abstract: The Witten-Reshetikhin-Turaev invariants of a 3-manifold are defined for each root of unity. Nevertheless their formulas depend significantly on the order of the root considered, hence appeared the need to unify these invariants. Over the years several such unified quantum invariants have been produced through a variety of methods (number-theoretical, analytic). The Habiro invariant for integral homology spheres taking values in the cyclotomic completion of the polynomial ring Z[q] allowed a better understanding of the WRT invariants. We will discuss the relation between Habiro's invariant and the known previous approaches (Ohtsuki's perturbative series, Lawrence's holomorphic invariant).
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