TY - JOUR AU - Hidalgo, Rubén A. PY - 2017/04/24 Y2 - 2024/03/28 TI - A commutator rigidity for function groups and Torelli’s theorem JF - Proyecciones (Antofagasta, On line) JA - Proyecciones (Antofagasta, On line) VL - 22 IS - 2 SE - DO - 10.4067/S0716-09172003000200002 UR - https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1486 SP - 117-125 AB - <p>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.</p> ER -