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

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

2008-01-25

arxiv.org/abs/0801.3893v3

Mathematics

Geometric Topology

31 pages, 18 Figures; Appendix substantially revised

Scientific paper

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. One of the applications are the new Ohtsuki series (perturbative expansions of I_M at roots of unity) dominating all quantum SO(3) invariants.

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