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

  • Part of
  • Anna Beliakova, Thang T. Q. Lê
  • Journal:
    Compositio Mathematica / Volume 143 / Issue 6 / November 2007
    Published online by Cambridge University Press:
    01 November 2007, pp. 1593-1612
    Print publication:
    November 2007
    • Article
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  • 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.