A commutator rigidity for function groups and Torelli’s theorem

Rubén 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:



H. Farkas and I. Kra. Riemann surfaces. Graduate Texts in Mathematics, Springer-Verlag.

R. Hidalgo. Homology coverings of Riemann surfaces, Tôhoku Math. J. 45 (1993), 499-503.

R. Hidalgo, Kleinian groups with common commutator subgroup, Complex variables 28, pp. 121-133, (1995).

R. Hidalgo. Noded Fuchsian groups, Complex Variables 36, pp. 45-66, (1998).

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

R. Hidalgo. Homology covering of closed Klein surfaces. Revista Proyecciones 18, pp. 165-173, (1999).

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

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

B. Markit. Kleinian Groups Grundlehren der Mathematischen Wissenschaften, Vol. 287, Springer-Verlag, (1988).

B. Maskit. On boundaries of Teichmüller spaces and on kleinian groups II, Ann. of Math. 91, pp. 607-639, (1970).

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

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