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Integrality of quantum 3-manifold invariants and a rational surgery formula


Beliakova, A; Lê, T T Q (2007). Integrality of quantum 3-manifold invariants and a rational surgery formula. Compositio Mathematica, 143(6):1593-1612.

Abstract

We prove that the Witten–Reshetikhin–Turaev (WRT) SO(3) invariant of an arbitrary 3-manifold M is always an algebraic integer. Moreover, we give a rational surgery formula for the unified invariant dominating WRT SO(3) invariants of rational homology 3-spheres at roots of unity of order co-prime with the torsion. As an application, we compute the unified invariant for Seifert fibered spaces and for Dehn surgeries on twist knots. We show that this invariant separates Seifert fibered integral homology spaces and can be used to detect the unknot.

Abstract

We prove that the Witten–Reshetikhin–Turaev (WRT) SO(3) invariant of an arbitrary 3-manifold M is always an algebraic integer. Moreover, we give a rational surgery formula for the unified invariant dominating WRT SO(3) invariants of rational homology 3-spheres at roots of unity of order co-prime with the torsion. As an application, we compute the unified invariant for Seifert fibered spaces and for Dehn surgeries on twist knots. We show that this invariant separates Seifert fibered integral homology spaces and can be used to detect the unknot.

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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:2007
Deposited On:07 Dec 2009 08:27
Last Modified:05 Apr 2016 13:23
Publisher:London Mathematical Society
ISSN:0010-437X
Publisher DOI:https://doi.org/10.1112/S0010437X07003053
Related URLs:http://arxiv.org/abs/math/0608627

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