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.

Resumen

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.

Citas

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

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

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

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

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

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

[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).

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

[10] B. Maskit. On boundaries of Teichmüller spaces and on kleinian groups II, Ann. of Math. 91, pp. 607-639, (1970).
Publicado
2017-04-24
Cómo citar
Hidalgo, R. (2017). A commutator rigidity for function groups and Torelli’s theorem. Proyecciones. Journal of Mathematics, 22(2), 117-125. https://doi.org/10.4067/S0716-09172003000200002
Sección
Artículos