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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Abstract

HIDALGO, RUBÉN. A COMMUTATOR RIGIDITY FOR FUNCTION GROUPS AND TORELLI’S THEOREM. Proyecciones (Antofagasta) [online]. 2003, vol.22, n.2, pp.117-125. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172003000200002.

We show that a non-elementary finitely generated torsion-free func-tion group is uniquely determined by its commutator subgroup. In this way, we obtain a generalization of the results obtained in [2], [3] and [8]. This is well related to Torelli’s theorem for closed Riemann sur-faces.For a general non-elementary torsion-free Kleinian group the above rigidity property still unknown

Keywords : Kleinian groups; Function groups; Torelli’s theorem; Hyperbolic 3-manifolds.

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