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.

THREE MANIFOLD INVARIANTS AND THEIR RELATION WITH THE FUNDAMENTAL GROUP

PILO, LUIGI
1998

Abstract

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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/20821
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