Anna Beliakova, Irmgard Buehler, Thang Le
Published 2008-01-25, updated 2009-05-16Version 3
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.
Comments: 31 pages, 18 Figures; Appendix substantially revised
Journal: Inventiones, Volume 185, Issue 1 (2011), Page 121-174
Unified Quantum SO(3) and SU(2) Invariants for Rational Homology 3-Spheres
On Perturbative PSU(n) Invariants of Rational Homology 3-Spheres
On intersection forms of definite 4-manifolds bounded by a rational homology 3-sphere
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