Three-manifold invariants and their relation with the fundamental group

Details Three-manifold invariants and their relation with the fundamental group Three-manifold invariants and their relation with the fundamental group

1996-12-09

arxiv.org/abs/hep-th/9612090v1

Commun.Math.Phys. 192 (1998) 47-65

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, Latex document, two eps figures

Scientific paper

10.1007/s002200050290

We consider the 3-manifold invariant I(M) which is defined by means of the Chern-Simons quantum field theory and which coincides with the Reshetikhin-Turaev invariant. We present some arguments and numerical results supporting the conjecture that, for nonvanishing I(M), the absolute value | I(M) | only depends on the fundamental group \pi_1 (M) of the manifold M. For lens spaces, the conjecture is proved when the gauge group is SU(2). In the case in which the gauge group is SU(3), we present numerical computations confirming the conjecture.

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