A commutator rigidity for function groups and Torelli’s theorem

  • Rubén A. Hidalgo Universidad Técnica Federico Santa María.
Palabras clave: Kleinian groups, Function groups, Torelli’s theorem, Hyperbolic 3-manifolds.


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.

Biografía del autor/a

Rubén A. Hidalgo, Universidad Técnica Federico Santa María.
Departamento de Matemática.


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[5] R. Hidalgo. Noded function groups. Contemporary Mathematics. 240, pp. 209-222, (1999).

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[7] R. Hidalgo. A note on the homology covering of analytically finite Klein surfaces. Complex variables 42, pp. 183-192, (2000).

[8] B. Maskit. The homology covering of a Riemann surface, Tôhoku Math. J. 38, pp. 561-562, (1986).

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[10] B. Maskit. On boundaries of Teichmüller spaces and on kleinian groups II, Ann. of Math. 91, pp. 607-639, (1970).
Cómo citar
Hidalgo, R. (2017). A commutator rigidity for function groups and Torelli’s theorem. Proyecciones. Revista De Matemática, 22(2), 117-125. https://doi.org/10.4067/S0716-09172003000200002