A Unified Quantum SO(3) Invariant for Rational Homology 3-Spheres
Geometric Topology
2015-05-13 v3 Quantum Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.0801.3893,
title = {A Unified Quantum SO(3) Invariant for Rational Homology 3-Spheres},
author = {Anna Beliakova and Irmgard Buehler and Thang Le},
journal= {arXiv preprint arXiv:0801.3893},
year = {2015}
}
Comments
31 pages, 18 Figures; Appendix substantially revised