Quantum Topology


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Volume 5, Issue 1, 2014, pp. 99–141
DOI: 10.4171/QT/48

Published online: 2014-03-03

On the integrality of the Witten–Reshetikhin–Turaev 3-manifold invariants

Anna Beliakova[1], Qi Chen[2] and Thang T. Q. Lê[3]

(1) University of Zurich
(2) Winston-Salem State University, USA
(3) Georgia Institute of Technology, Atlanta, USA

We prove that the SU(2) Witten–Reshetikhin–Turaev invariant of any 3-manifold with any colored link inside at any root of unity is an algebraic integer. As a byproduct, we get a new proof of the integrality of the SO(3) Witten–Reshetikhin–Turaev invariant for any 3-manifold with any colored link inside at any root of unity of odd order.

Keywords: Witten–Reshetikhin–Turaev invariants, 3-manifolds, colored links

Beliakova Anna, Chen Qi, Lê Thang T. Q.: On the integrality of the Witten–Reshetikhin–Turaev 3-manifold invariants. Quantum Topol. 5 (2014), 99-141. doi: 10.4171/QT/48