A commutator rigidity for function groups and Torelli’s theorem
Hidalgo, Rubén A.
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 ,  and . 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.