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


Beliakova, A; Blanchet, C; Lê, T T (2008). Unified quantum invariants and their refinements for homology 3-spheres with 2-torsion. Fundamenta Mathematicae, 201(3):217-239.

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.
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.

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.
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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2008
Deposited On:06 Feb 2009 07:47
Last Modified:05 Apr 2016 12:57
Publisher:Polska Akademia Nauk, Instytut Matematyczny
ISSN:0016-2736
Publisher DOI:https://doi.org/10.4064/fm201-3-2
Related URLs:http://arxiv.org/abs/0704.3669v1

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