A commutator rigidity for function groups and Torelli’s theorem

Rubén A. Hidalgo


We show that a non-elementary finitely generated torsion-free function 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 surfaces. For a general non-elementary torsion-free Kleinian group the above rigidity property still unknown.

Palabras clave

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

Texto completo:



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DOI: http://dx.doi.org/10.4067/S0716-09172003000200002

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