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

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. DOI: https://doi.org/10.4171/QT/48 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-98947 Published Version Originally published at: Beliakova, Anna; Chen, Qi; Le, Thang (2014). On the integrality of Witten-Reshetikhin-Turaev 3manifold invariants. Quantum Topology, 5(1):99-141. DOI: https://doi.org/10.4171/QT/48 Quantum Topol. 5 (2014), 99–141 DOI 10.4171/QT/48 Quantum Topology © European Mathematical Society On the integrality of the Witten–Reshetikhin–Turaev 3-manifold invariants Anna Beliakova, Qi Chen, and Thang Le Abstract. 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. 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. Mathematics Subject Classification (2010). 57M27; 57M25.