Communications in Mathematical Physics

, Volume 192, Issue 1, pp 47–65 | Cite as

Three-Manifold Invariants and Their Relation with the Fundamental Group

  • E. Guadagnini
  • L. Pilo


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 π1 (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.


Manifold Field Theory Numerical Computation Quantum Field Theory Gauge Group 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • E. Guadagnini
    • 1
  • L. Pilo
    • 2
  1. 1.Dipartimento di Fisica dell'Università di Pisa, Piazza Torricelli, 2, 56100 Pisa. Italy.¶E-mail: guadagni@ipifidpt.difi.unipi.itIT
  2. 2.Scuola Normale Superiore, Piazza dei Cavalieri 7, 56100 Pisa, Italy. E-mail: pilo@ibmth.difi.unipi.itIT

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