Unified quantum invariants and their refinements for homology 3-spheres with 2-torsion

Anna Beliakova, Christian Blanchet, and Thang T. Q. Lê. "Unified quantum invariants and their refinements for homology 3-spheres with 2-torsion." Fundamenta Mathematicae 201.3 (2008): 217-239. <http://eudml.org/doc/282946>.

@article{AnnaBeliakova2008,
abstract = {For every rational homology 3-sphere with H₁(M,ℤ) = (ℤ/2ℤ)ⁿ we construct a unified invariant (which takes values in a certain cyclotomic completion of a polynomial ring) such that the evaluation of this invariant at any odd root of unity provides the SO(3) Witten-Reshetikhin-Turaev invariant at this root, and at any even root of unity the SU(2) quantum invariant. Moreover, this unified invariant splits into a sum of the refined unified invariants dominating spin and cohomological refinements of quantum SU(2) invariants. New results on the Ohtsuki series and the integrality of quantum invariants are the main applications of our construction.},
author = {Anna Beliakova, Christian Blanchet, Thang T. Q. Lê},
journal = {Fundamenta Mathematicae},
keywords = {quantum invariants; Jones polynomial; Ohtsuki series; cyclotomic completion ring; -hypergeometric series},
language = {eng},
number = {3},
pages = {217-239},
title = {Unified quantum invariants and their refinements for homology 3-spheres with 2-torsion},
url = {http://eudml.org/doc/282946},
volume = {201},
year = {2008},
}

TY - JOUR
AU - Anna Beliakova
AU - Christian Blanchet
AU - Thang T. Q. Lê
TI - Unified quantum invariants and their refinements for homology 3-spheres with 2-torsion
JO - Fundamenta Mathematicae
PY - 2008
VL - 201
IS - 3
SP - 217
EP - 239
AB - For every rational homology 3-sphere with H₁(M,ℤ) = (ℤ/2ℤ)ⁿ we construct a unified invariant (which takes values in a certain cyclotomic completion of a polynomial ring) such that the evaluation of this invariant at any odd root of unity provides the SO(3) Witten-Reshetikhin-Turaev invariant at this root, and at any even root of unity the SU(2) quantum invariant. Moreover, this unified invariant splits into a sum of the refined unified invariants dominating spin and cohomological refinements of quantum SU(2) invariants. New results on the Ohtsuki series and the integrality of quantum invariants are the main applications of our construction.
LA - eng
KW - quantum invariants; Jones polynomial; Ohtsuki series; cyclotomic completion ring; -hypergeometric series
UR - http://eudml.org/doc/282946
ER -