Integrality of quantum 3-manifold invariants and rational surgery formula

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

2006-08-25

arxiv.org/abs/math/0608627v2

Mathematics

Geometric Topology

18 pages, Compositio Math. in press

Scientific paper

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 integral homology Seifert fibered spaces and can be used to detect the unknot.

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