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A simple proof of integrality of quantum invariants at prime roots of unity

Published online by Cambridge University Press:  01 May 1997

G. MASBAUM  and
J. D. ROBERTS
G. MASBAUM
Affiliation:
CNRS, Institut de Mathématiques de Jussieu (Equipe ‘Théories Géométriques’), Université Paris VII, Case 7012, 2 pl. Jussieu, 75251 PARIS Cedex 05, France. E-mail: [email protected]
J. D. ROBERTS
Affiliation:
Current address: Department of Mathematics and Statistics, Edinburgh University, Edinburgh EH9 3JZ. E-mail: [email protected] Mathematics Department, Evans Hall, UC Berkeley, CA 94720-3840, USA
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Abstract

Recently, Hitoshi Murakami has shown that the quantum SU(2)- and SO(3)-invariants of 3-manifolds at roots of unity of prime order are algebraic integers. Unfortunately, his proof is by a very complicated computation. Here, a quite different and very simple proof is presented, based on the second author's method to show that the Turaev–Viro invariant is the square of the modulus of the Reshetikhin–Turaev invariant.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 121 , Issue 3 , May 1997 , pp. 443 - 454
Copyright
Cambridge Philosophical Society 1997

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